Scippy

SCIP

Solving Constraint Integer Programs

cons_nonlinear.h
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4 /* SCIP --- Solving Constraint Integer Programs */
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24 
25 /**@file cons_nonlinear.h
26  * @ingroup CONSHDLRS
27  * @brief constraint handler for nonlinear constraints specified by algebraic expressions
28  * @author Ksenia Bestuzheva
29  * @author Benjamin Mueller
30  * @author Felipe Serrano
31  * @author Stefan Vigerske
32  *
33  * For additional documentation on this constraint handler, see also the SCIP 8 release report.
34  */
35 
36 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
37 
38 #ifndef __SCIP_CONS_NONLINEAR_H__
39 #define __SCIP_CONS_NONLINEAR_H__
40 
41 
42 #include "scip/scip.h"
43 #include "scip/type_nlhdlr.h"
44 
45 #ifdef __cplusplus
46 extern "C" {
47 #endif
48 
49 /**@addtogroup CONSHDLRS
50  * @{
51  *
52  * @name Nonlinear Constraints
53  * @{
54  */
55 
56 /** linear auxiliary expression of the form xy {≤,≥,=} coefs[0]w + coefs[1]x + coefs[2]y + cst */
58 {
59  SCIP_Real coefs[3]; /**< coefficients in the auxiliary expression */
60  SCIP_Real cst; /**< constant */
61  SCIP_VAR* auxvar; /**< auxiliary variable w in xy {&le;,&ge;,=} auxexpr(w, x, y) */
62  SCIP_Bool underestimate; /**< whether the auxexpr underestimates the product */
63  SCIP_Bool overestimate; /**< whether the auxexpr overestimates the product */
64 };
66 
67 /** bilinear term structure
68  *
69  * This can represent a product which
70  * - explicitly exists in the problem and is under- and/or overestimated by a single auxiliary variable
71  * stored as `var` in the union `aux` (case `nauxexprs` = 0) or
72  * - is involved in bilinear relations implicitly given by linear constraints with binary variables, and
73  * is under- and/or overestimated by linear expression(s) stored as `exprs` in the union `aux` (case `nauxexprs` > 0).
74  *
75  * An explicitly existing product can also be involved in implicit relations, then it will be stored as in
76  * the second case.
77  */
79 {
80  SCIP_VAR* x; /**< first variable */
81  SCIP_VAR* y; /**< second variable */
82  union
83  {
84  SCIP_CONSNONLINEAR_AUXEXPR** exprs; /**< auxiliary expressions for the implicit product of x and y */
85  SCIP_VAR* var; /**< auxiliary variable for the explicit product of x and y */
86  } aux;
87  int nauxexprs; /**< number of aux.exprs (0 for products without implicit relations) */
88  int auxexprssize; /**< size of the aux.exprs array */
89  int nlockspos; /**< number of positive expression locks */
90  int nlocksneg; /**< number of negative expression locks */
91  SCIP_Bool existing; /**< does the product exist explicitly in the problem? */
92 };
93 typedef struct SCIP_ConsNonlinear_BilinTerm SCIP_CONSNONLINEAR_BILINTERM; /**< bilinear term structure */
94 
95 /** evaluation callback for (vertex-polyhedral) functions used as input for facet computation of its envelopes
96  *
97  * \param[in] args the point to be evaluated
98  * \param[in] nargs the number of arguments of the function (length of array `args`)
99  * \param[in] funcdata user-data of function evaluation callback
100  * \return value of function in point given by `args` or SCIP_INVALID if could not be evaluated
101  */
102 #define SCIP_DECL_VERTEXPOLYFUN(f) SCIP_Real f (SCIP_Real* args, int nargs, void* funcdata)
103 
104 /** maximum dimension of vertex-polyhedral function for which we can try to compute a facet of its convex or concave envelope */
105 #define SCIP_MAXVERTEXPOLYDIM 14
106 
107 /** upgrading method for nonlinear constraints into more specific constraints
108  *
109  * The method might upgrade a nonlinear constraint into a set of upgrade constraints.
110  * The caller provided an array `upgdconss` of size `upgdconsssize` to store upgrade constraints.
111  * If an upgrade is not possible, set `*nupgdconss` to zero.
112  * If more than `upgdconsssize` many constraints shall replace `cons`, the function
113  * should return the required number as negated value in `*nupgdconss`,
114  * e.g., if `cons` should be replaced by 3 constraints, the function should set
115  * `*nupgdconss` to -3 and return with SCIP_OKAY.
116  *
117  * \param[in] scip SCIP main data structure
118  * \param[in] cons the nonlinear constraint to upgrade
119  * \param[in] nvarexprs total number of variable expressions in the nonlinear constraint
120  * \param[out] nupgdconss pointer to store number of constraints that replace this constraint
121  * \param[out] upgdconss array to store constraints that replace this constraint
122  * \param[in] upgdconsssize length of the provided `upgdconss` array
123  */
124 #define SCIP_DECL_NONLINCONSUPGD(x) SCIP_RETCODE x (SCIP* scip, SCIP_CONS* cons, int nvarexprs, \
125  int* nupgdconss, SCIP_CONS** upgdconss, int upgdconsssize)
126 
127 /** @} */
128 /** @} */
129 
130 /** creates the handler for nonlinear constraints and includes it in SCIP
131  *
132  * @ingroup ConshdlrIncludes
133  */
134 SCIP_EXPORT
136  SCIP* scip /**< SCIP data structure */
137  );
138 
139 /**@addtogroup CONSHDLRS
140  *
141  * @{
142  *
143  * @name Nonlinear Constraints
144  *
145  * @{
146  */
147 
148 /* Nonlinear Constraint Handler Methods */
149 
150 /** includes a nonlinear constraint upgrade method into the nonlinear constraint handler */
151 SCIP_EXPORT
153  SCIP* scip, /**< SCIP data structure */
154  SCIP_DECL_NONLINCONSUPGD((*nlconsupgd)), /**< method to call for upgrading nonlinear constraint */
155  int priority, /**< priority of upgrading method */
156  SCIP_Bool active, /**< should the upgrading method by active by default? */
157  const char* conshdlrname /**< name of the constraint handler */
158  );
159 
160 /** creates and captures a nonlinear constraint
161  *
162  * @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
163  */
164 SCIP_EXPORT
166  SCIP* scip, /**< SCIP data structure */
167  SCIP_CONS** cons, /**< pointer to hold the created constraint */
168  const char* name, /**< name of constraint */
169  SCIP_EXPR* expr, /**< expression of constraint (must not be NULL) */
170  SCIP_Real lhs, /**< left hand side of constraint */
171  SCIP_Real rhs, /**< right hand side of constraint */
172  SCIP_Bool initial, /**< should the LP relaxation of constraint be in the initial LP?
173  * Usually set to TRUE. Set to FALSE for 'lazy constraints'. */
174  SCIP_Bool separate, /**< should the constraint be separated during LP processing?
175  * Usually set to TRUE. */
176  SCIP_Bool enforce, /**< should the constraint be enforced during node processing?
177  * TRUE for model constraints, FALSE for additional, redundant constraints. */
178  SCIP_Bool check, /**< should the constraint be checked for feasibility?
179  * TRUE for model constraints, FALSE for additional, redundant constraints. */
180  SCIP_Bool propagate, /**< should the constraint be propagated during node processing?
181  * Usually set to TRUE. */
182  SCIP_Bool local, /**< is constraint only valid locally?
183  * Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. */
184  SCIP_Bool modifiable, /**< is constraint modifiable (subject to column generation)?
185  * Usually set to FALSE. In column generation applications, set to TRUE if pricing
186  * adds coefficients to this constraint. */
187  SCIP_Bool dynamic, /**< is constraint subject to aging?
188  * Usually set to FALSE. Set to TRUE for own cuts which
189  * are separated as constraints. */
190  SCIP_Bool removable /**< should the relaxation be removed from the LP due to aging or cleanup?
191  * Usually set to FALSE. Set to TRUE for 'lazy constraints' and 'user cuts'. */
192  );
193 
194 /** creates and captures a nonlinear constraint with all its constraint flags set to their default values
195  *
196  * All flags can be set via SCIPconsSetFLAGNAME-methods.
197  *
198  * @see SCIPcreateConsNonlinear() for information about the basic constraint flag configuration.
199  *
200  * @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
201  */
202 SCIP_EXPORT
204  SCIP* scip, /**< SCIP data structure */
205  SCIP_CONS** cons, /**< pointer to hold the created constraint */
206  const char* name, /**< name of constraint */
207  SCIP_EXPR* expr, /**< expression of constraint (must not be NULL) */
208  SCIP_Real lhs, /**< left hand side of constraint */
209  SCIP_Real rhs /**< right hand side of constraint */
210  );
211 
212 /** creates and captures a quadratic nonlinear constraint
213  *
214  * @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
215  */
216 SCIP_EXPORT
218  SCIP* scip, /**< SCIP data structure */
219  SCIP_CONS** cons, /**< pointer to hold the created constraint */
220  const char* name, /**< name of constraint */
221  int nlinvars, /**< number of linear terms */
222  SCIP_VAR** linvars, /**< array with variables in linear part */
223  SCIP_Real* lincoefs, /**< array with coefficients of variables in linear part */
224  int nquadterms, /**< number of quadratic terms */
225  SCIP_VAR** quadvars1, /**< array with first variables in quadratic terms */
226  SCIP_VAR** quadvars2, /**< array with second variables in quadratic terms */
227  SCIP_Real* quadcoefs, /**< array with coefficients of quadratic terms */
228  SCIP_Real lhs, /**< left hand side of quadratic equation */
229  SCIP_Real rhs, /**< right hand side of quadratic equation */
230  SCIP_Bool initial, /**< should the LP relaxation of constraint be in the initial LP?
231  * Usually set to TRUE. Set to FALSE for 'lazy constraints'. */
232  SCIP_Bool separate, /**< should the constraint be separated during LP processing?
233  * Usually set to TRUE. */
234  SCIP_Bool enforce, /**< should the constraint be enforced during node processing?
235  * TRUE for model constraints, FALSE for additional, redundant constraints. */
236  SCIP_Bool check, /**< should the constraint be checked for feasibility?
237  * TRUE for model constraints, FALSE for additional, redundant constraints. */
238  SCIP_Bool propagate, /**< should the constraint be propagated during node processing?
239  * Usually set to TRUE. */
240  SCIP_Bool local, /**< is constraint only valid locally?
241  * Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. */
242  SCIP_Bool modifiable, /**< is constraint modifiable (subject to column generation)?
243  * Usually set to FALSE. In column generation applications, set to TRUE if pricing
244  * adds coefficients to this constraint. */
245  SCIP_Bool dynamic, /**< is constraint subject to aging?
246  * Usually set to FALSE. Set to TRUE for own cuts which
247  * are separated as constraints. */
248  SCIP_Bool removable /**< should the relaxation be removed from the LP due to aging or cleanup?
249  * Usually set to FALSE. Set to TRUE for 'lazy constraints' and 'user cuts'. */
250  );
251 
252 /** creates and captures a quadratic nonlinear constraint with all its constraint flags set to their default values
253  *
254  * All flags can be set via SCIPconsSetFLAGNAME-methods.
255  *
256  * @see SCIPcreateConsQuadraticNonlinear() for information about the basic constraint flag configuration.
257  *
258  * @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
259  */
260 SCIP_EXPORT
262  SCIP* scip, /**< SCIP data structure */
263  SCIP_CONS** cons, /**< pointer to hold the created constraint */
264  const char* name, /**< name of constraint */
265  int nlinvars, /**< number of linear terms */
266  SCIP_VAR** linvars, /**< array with variables in linear part */
267  SCIP_Real* lincoefs, /**< array with coefficients of variables in linear part */
268  int nquadterms, /**< number of quadratic terms */
269  SCIP_VAR** quadvars1, /**< array with first variables in quadratic terms */
270  SCIP_VAR** quadvars2, /**< array with second variables in quadratic terms */
271  SCIP_Real* quadcoefs, /**< array with coefficients of quadratic terms */
272  SCIP_Real lhs, /**< left hand side of quadratic equation */
273  SCIP_Real rhs /**< right hand side of quadratic equation */
274  );
275 
276 /** creates and captures a nonlinear constraint that is a second-order cone constraint with all its constraint flags set to their default values
277  *
278  * \f$\sqrt{\gamma + \sum_{i=1}^{n} (\alpha_i\, (x_i + \beta_i))^2} \leq \alpha_{n+1}\, (x_{n+1}+\beta_{n+1})\f$
279  *
280  * @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
281  */
282 SCIP_EXPORT
284  SCIP* scip, /**< SCIP data structure */
285  SCIP_CONS** cons, /**< pointer to hold the created constraint */
286  const char* name, /**< name of constraint */
287  int nvars, /**< number of variables on left hand side of constraint (n) */
288  SCIP_VAR** vars, /**< array with variables on left hand side (x_i) */
289  SCIP_Real* coefs, /**< array with coefficients of left hand side variables (alpha_i), or NULL if all 1.0 */
290  SCIP_Real* offsets, /**< array with offsets of variables (beta_i), or NULL if all 0.0 */
291  SCIP_Real constant, /**< constant on left hand side (gamma) */
292  SCIP_VAR* rhsvar, /**< variable on right hand side of constraint (x_{n+1}) */
293  SCIP_Real rhscoeff, /**< coefficient of variable on right hand side (alpha_{n+1}) */
294  SCIP_Real rhsoffset /**< offset of variable on right hand side (beta_{n+1}) */
295  );
296 
297 /** creates and captures a signpower nonlinear constraint with all its constraint flags set to their default values
298  *
299  * \f$\textrm{lhs} \leq \textrm{sign}(x+a) |x+a|^n + c z \leq \textrm{rhs}\f$
300  *
301  * @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
302  */
303 SCIP_EXPORT
305  SCIP* scip, /**< SCIP data structure */
306  SCIP_CONS** cons, /**< pointer to hold the created constraint */
307  const char* name, /**< name of constraint */
308  SCIP_VAR* x, /**< nonlinear variable x in constraint */
309  SCIP_VAR* z, /**< linear variable z in constraint */
310  SCIP_Real exponent, /**< exponent n of |x+offset|^n term in constraint */
311  SCIP_Real xoffset, /**< offset in |x+offset|^n term in constraint */
312  SCIP_Real zcoef, /**< coefficient of z in constraint */
313  SCIP_Real lhs, /**< left hand side of constraint */
314  SCIP_Real rhs /**< right hand side of constraint */
315  );
316 
317 /** gets tag indicating current local variable bounds */
318 SCIP_EXPORT
320  SCIP_CONSHDLR* conshdlr /**< nonlinear constraint handler */
321  );
322 
323 /** gets the `curboundstag` from the last time where variable bounds were relaxed */
324 SCIP_EXPORT
326  SCIP_CONSHDLR* conshdlr /**< nonlinear constraint handler */
327  );
328 
329 /** increments `curboundstag` and resets `lastboundrelax` in constraint handler data
330  *
331  * @attention This method is not intended for normal use.
332  * These tags are maintained by the event handler for variable bound change events.
333  * This method is used by some unittests.
334  */
335 SCIP_EXPORT
337  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
338  SCIP_Bool boundrelax /**< indicates whether a bound was relaxed, i.e., lastboundrelax should be set too */
339  );
340 
341 /** returns the hashmap that is internally used to map variables to their corresponding variable expressions */
342 SCIP_EXPORT
344  SCIP_CONSHDLR* conshdlr /**< nonlinear constraint handler */
345  );
346 
347 /** processes a rowprep for cut addition and maybe report branchscores */
348 SCIP_EXPORT
350  SCIP* scip, /**< SCIP data structure */
351  SCIP_NLHDLR* nlhdlr, /**< nonlinear handler which provided the estimator */
352  SCIP_CONS* cons, /**< nonlinear constraint */
353  SCIP_EXPR* expr, /**< expression */
354  SCIP_ROWPREP* rowprep, /**< cut to be added */
355  SCIP_Bool overestimate, /**< whether the expression needs to be over- or underestimated */
356  SCIP_VAR* auxvar, /**< auxiliary variable */
357  SCIP_Real auxvalue, /**< current value of expression w.r.t. auxiliary variables as obtained from EVALAUX */
358  SCIP_Bool allowweakcuts, /**< whether we should only look for "strong" cuts, or anything that separates is fine */
359  SCIP_Bool branchscoresuccess, /**< whether the estimator generation generated branching scores */
360  SCIP_Bool inenforcement, /**< whether we are in enforcement, or only in separation */
361  SCIP_SOL* sol, /**< solution to be separated (NULL for the LP solution) */
362  SCIP_RESULT* result /**< pointer to store the result */
363  );
364 
365 /** returns whether all nonlinear constraints are assumed to be convex */
366 SCIP_EXPORT
368  SCIP_CONSHDLR* conshdlr
369  );
370 
371 /** collects all bilinear terms for a given set of constraints
372  *
373  * @attention This method should only be used for unit tests that depend on SCIPgetBilinTermsNonlinear(),
374  * SCIPgetBilinTermNonlinear() or SCIPgetBilinTermIdxNonlinear().
375  */
376 SCIP_EXPORT
378  SCIP* scip, /**< SCIP data structure */
379  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
380  SCIP_CONS** conss, /**< nonlinear constraints */
381  int nconss /**< total number of nonlinear constraints */
382  );
383 
384 /** returns the total number of bilinear terms that are contained in all nonlinear constraints
385  *
386  * @note This method should only be used after auxiliary variables have been created, i.e., after CONSINITLP.
387  */
388 SCIP_EXPORT
390  SCIP_CONSHDLR* conshdlr /**< nonlinear constraint handler */
391  );
392 
393 /** returns all bilinear terms that are contained in all nonlinear constraints
394  *
395  * @note This method should only be used after auxiliary variables have been created, i.e., after CONSINITLP.
396  * @note The value of the auxiliary variable of a bilinear term might be NULL, which indicates that the term does not have an auxiliary variable.
397  */
398 SCIP_EXPORT
400  SCIP_CONSHDLR* conshdlr /**< nonlinear constraint handler */
401  );
402 
403 /** returns the index of the bilinear term representing the product of the two given variables
404  *
405  * @note The method should only be used after auxiliary variables have been created, i.e., after CONSINITLP.
406  * @return The method returns -1 if the variables do not appear bilinearly.
407  */
408 SCIP_EXPORT
410  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
411  SCIP_VAR* x, /**< first variable */
412  SCIP_VAR* y /**< second variable */
413  );
414 
415 /** returns the bilinear term that represents the product of two given variables
416  *
417  * @note The method should only be used after auxiliary variables have been created, i.e., after CONSINITLP.
418  * @return The method returns NULL if the variables do not appear bilinearly.
419  */
420 SCIP_EXPORT
422  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
423  SCIP_VAR* x, /**< first variable */
424  SCIP_VAR* y /**< second variable */
425  );
426 
427 /** evaluates an auxiliary expression for a bilinear term */
428 SCIP_EXPORT
430  SCIP* scip, /**< SCIP data structure */
431  SCIP_VAR* x, /**< first variable of the bilinear term */
432  SCIP_VAR* y, /**< second variable of the bilinear term */
433  SCIP_CONSNONLINEAR_AUXEXPR* auxexpr, /**< auxiliary expression */
434  SCIP_SOL* sol /**< solution at which to evaluate (can be NULL) */
435  );
436 
437 /** stores the variables of a bilinear term in the data of the constraint handler */
438 SCIP_EXPORT
440  SCIP* scip, /**< SCIP data structure */
441  SCIP_CONSHDLR* conshdlr, /**< constraint handler */
442  SCIP_VAR* x, /**< first variable */
443  SCIP_VAR* y, /**< second variable */
444  SCIP_VAR* auxvar, /**< auxiliary variable (might be NULL) */
445  int nlockspos, /**< number of positive expression locks */
446  int nlocksneg /**< number of negative expression locks */
447  );
448 
449 /** stores the variables of a bilinear term in the data of the constraint handler */
450 SCIP_EXPORT
452  SCIP* scip, /**< SCIP data structure */
453  SCIP_CONSHDLR* conshdlr, /**< constraint handler */
454  SCIP_VAR* x, /**< first variable */
455  SCIP_VAR* y, /**< second variable */
456  SCIP_VAR* auxvar, /**< auxiliary variable (might be NULL) */
457  SCIP_Real coefx, /**< coefficient of x in the auxiliary expression */
458  SCIP_Real coefy, /**< coefficient of y in the auxiliary expression */
459  SCIP_Real coefaux, /**< coefficient of auxvar in the auxiliary expression */
460  SCIP_Real cst, /**< constant of the auxiliary expression */
461  SCIP_Bool overestimate /**< whether the auxiliary expression overestimates the bilinear product */
462  );
463 
464 /** computes a facet of the convex or concave envelope of a vertex polyhedral function
465  *
466  * If \f$ f(x) \f$ is vertex-polyhedral, then \f$ g \f$ is a convex underestimator if and only if
467  * \f$ g(v^i) \leq f(v^i), \forall i \f$, where \f$ \{ v^i \}_{i = 1}^{2^n} \subseteq \mathbb R^n \f$ are the vertices
468  * of the domain of \f$ x \f$, \f$ [\ell,u] \f$. Hence, we can compute a linear underestimator by solving the following
469  * LP (we don't necessarily get a facet of the convex envelope, see below):
470  *
471  * \f{align*}{
472  * \max \, & \alpha^T x^* + \beta \\
473  * s.t. \; & \alpha^T v^i + \beta \le f(v^i), \, \forall i = 1, \ldots, 2^n
474  * \f}
475  *
476  * In principle, one would need to update the LP whenever the domain changes. However, \f$ [\ell,u] = T([0, 1]^n) \f$,
477  * where \f$ T \f$ is an affine linear invertible transformation given by \f$ T(y)_i = (u_i - \ell_i) y_i + \ell_i \f$.
478  * Working with the change of variables \f$ x = T(y) \f$ allows us to keep the constraints of the LP, even if the domain
479  * changes. Indeed, after the change of variables, the problem is: find an affine underestimator \f$ g \f$ such that \f$
480  * g(T(y)) \le f(T(y)) \f$, for all \f$ y \in [0, 1]^n \f$. Now \f$ f(T(y)) \f$ is componentwise affine, but still
481  * satisfies that \f$ g \f$ is a valid underestimator if and only if \f$ g(T(u)) \leq f(T(u)), \forall u \in \{0, 1\}^n
482  * \f$. So we now look for \f$ \bar g(y) := g(T(y)) = g(((u_i - \ell_i) y_i + \ell_i)_i) = \bar \alpha^T y + \bar \beta
483  * \f$, where \f$ \bar \alpha_i = (u_i - \ell_i) \alpha_i \f$ and \f$ \bar \beta = \sum_i \alpha_i \ell_i + \beta \f$. So
484  * we find \f$ \bar g \f$ by solving the LP:
485  *
486  * \f{align*}{
487  * \max \, & \bar \alpha^T T^{-1}(x^*) + \bar \beta \\
488  * s.t. \; & \bar \alpha^T u + \bar \beta \le f(T(u)), \, \forall u \in \{0, 1\}^n
489  * \f}
490  *
491  * and recover \f$ g \f$ by calculating \f$ \bar \alpha_i = (u_i - \ell_i) \alpha_i, \bar \beta = \sum_i \alpha_i \ell_i +
492  * \beta \f$. Notice that \f$ f(T(u^i)) = f(v^i) \f$ so the right hand side doesn't change after the change of variables.
493  *
494  * Furthermore, the LP has more constraints than variables, so we solve its dual:
495  * \f{align*}{
496  * \min \, & \sum_i \lambda_i f(v^i) \\
497  * s.t. \; & \sum_i \lambda_i u^i = T^{-1}(x^*) \\
498  * & \sum_i \lambda_i = 1 \\
499  * & \forall i, \, \lambda_i \geq 0
500  * \f}
501  *
502  * In case we look for an overestimate, we do exactly the same, but have to maximize in the dual LP instead
503  * of minimize.
504  *
505  * #### Technical and implementation details
506  * -# \f$ U \f$ has exponentially many variables, so we only apply this separator for \f$n\f$ &le; \ref SCIP_MAXVERTEXPOLYDIM.
507  * -# If the bounds are not finite, there is no underestimator. Also, \f$ T^{-1}(x^*) \f$ must be in the domain,
508  * otherwise the dual is infeasible.
509  * -# After a facet is computed, we check whether it is a valid facet (i.e. we check \f$ \alpha^T v + \beta \le f(v) \f$
510  * for every vertex \f$ v \f$). If we find a violation of at most ADJUSTFACETFACTOR * SCIPlpfeastol(), then we weaken \f$
511  * \beta \f$ by this amount, otherwise, we discard the cut.
512  * -# If a variable is fixed within tolerances, we replace it with its value and compute the facet of the remaining
513  * expression. Note that since we are checking the cut for validity, this will never produce wrong result.
514  * -# If \f$ x^* \f$ is in the boundary of the domain, then the LP has infinitely many solutions, some of which might
515  * have very bad numerical properties. For this reason, we perturb \f$ x^* \f$ to be in the interior of the region.
516  * Furthermore, for some interior points, there might also be infinitely many solutions (e.g. for \f$ x y \f$ in \f$
517  * [0,1]^2 \f$ any point \f$ (x^*, y^*) \f$ such that \f$ y^* = 1 - x^* \f$ has infinitely many solutions). For this
518  * reason, we perturb any given \f$ x^* \f$. The idea is to try to get a facet of the convex/concave envelope. This only
519  * happens when the solution has \f$ n + 1 \f$ non zero \f$ \lambda \f$'s (i.e. the primal has a unique solution).
520  * -# We need to compute \f$ f(v^i) \f$ for every vertex of \f$ [\ell,u] \f$. A vertex is encoded by a number between 0
521  * and \f$ 2^n - 1 \f$, via its binary representation (0 bit is lower bound, 1 bit is upper bound), so we can compute
522  * all these values by iterating between 0 and \f$ 2^n - 1 \f$.
523  * -# To check that the computed cut is valid we do the following: we use a gray code to loop over the vertices
524  * of the box domain w.r.t. unfixed variables in order to evaluate the underestimator. To ensure the validity of the
525  * underestimator, we check whether \f$ \alpha v^i + \beta \le f(v^i) \f$ for every vertex \f$ v^i \f$ and adjust
526  * \f$ \beta \f$ if the maximal violation is small.
527  *
528  * @todo the solution is a facet if all variables of the primal have positive reduced costs (i.e. the solution is
529  * unique). In the dual, this means that there are \f$ n + 1 \f$ variables with positive value. Can we use this or some
530  * other information to handle any of both cases (point in the boundary or point in the intersection of polytopes
531  * defining different pieces of the convex envelope)? In the case where the point is in the boundary, can we use that
532  * information to maybe solve another to find a facet? How do the polytopes defining the pieces where the convex
533  * envelope is linear looks like, i.e, given a point in the interior of a facet of the domain, does the midpoint of the
534  * segment joining \f$ x^* \f$ with the center of the domain, always belongs to the interior of one of those polytopes?
535  */
536 SCIP_EXPORT
538  SCIP* scip, /**< SCIP data structure */
539  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
540  SCIP_Bool overestimate, /**< whether to compute facet of concave (TRUE) or convex (FALSE) envelope */
541  SCIP_DECL_VERTEXPOLYFUN((*function)), /**< pointer to vertex polyhedral function */
542  void* fundata, /**< data for function evaluation (can be NULL) */
543  SCIP_Real* xstar, /**< point to be separated */
544  SCIP_Real* box, /**< box where to compute facet: should be lb_1, ub_1, lb_2, ub_2... */
545  int nallvars, /**< half of the length of box */
546  SCIP_Real targetvalue, /**< target value: no need to compute facet if value in xstar would be worse than this value */
547  SCIP_Bool* success, /**< buffer to store whether a facet could be computed successfully */
548  SCIP_Real* facetcoefs, /**< buffer to store coefficients of facet defining inequality; must be an array of length at least nallvars */
549  SCIP_Real* facetconstant /**< buffer to store constant part of facet defining inequality */
550  );
551 
552 
553 /* Nonlinear Constraint Methods */
554 
555 /** returns the expression of the given nonlinear constraint */
556 SCIP_EXPORT
558  SCIP_CONS* cons /**< constraint data */
559  );
560 
561 /** gets the left hand side of a nonlinear constraint */
562 SCIP_EXPORT
564  SCIP_CONS* cons /**< constraint data */
565  );
566 
567 /** gets the right hand side of a nonlinear constraint */
568 SCIP_EXPORT
570  SCIP_CONS* cons /**< constraint data */
571  );
572 
573 /** gets the nonlinear constraint as a nonlinear row representation. */
574 SCIP_EXPORT
576  SCIP* scip, /**< SCIP data structure */
577  SCIP_CONS* cons, /**< constraint */
578  SCIP_NLROW** nlrow /**< pointer to store nonlinear row */
579  );
580 
581 /** returns the curvature of the expression of a given nonlinear constraint
582  *
583  * @note The curvature information is computed during CONSINITSOL.
584  */
585 SCIP_EXPORT
587  SCIP_CONS* cons /**< constraint data */
588  );
589 
590 /** checks whether expression of constraint can be represented as quadratic form
591  *
592  * Only sets `*isquadratic` to TRUE if the whole expression is quadratic (in the non-extended formulation) and non-linear.
593  * That is, the expression in each \ref SCIP_QUADEXPR_QUADTERM will be a variable expressions and
594  * \ref SCIPgetVarExprVar() can be used to retrieve the variable.
595  */
596 SCIP_EXPORT
598  SCIP* scip, /**< SCIP data structure */
599  SCIP_CONS* cons, /**< constraint data */
600  SCIP_Bool* isquadratic /**< buffer to store whether constraint is quadratic */
601  );
602 
603 /** changes left-hand-side of a nonlinear constraint
604  *
605  * @attention This method can only be called in the problem stage.
606  */
607 SCIP_EXPORT
609  SCIP* scip, /**< SCIP data structure */
610  SCIP_CONS* cons, /**< constraint data */
611  SCIP_Real lhs /**< new left-hand-side */
612  );
613 
614 /** changes right-hand-side of a nonlinear constraint
615  *
616  * @attention This method can only be called in the problem stage.
617  */
618 SCIP_EXPORT
620  SCIP* scip, /**< SCIP data structure */
621  SCIP_CONS* cons, /**< constraint data */
622  SCIP_Real rhs /**< new right-hand-side */
623  );
624 
625 /** changes expression of a nonlinear constraint
626  *
627  * @attention This method can only be called in the problem stage.
628  */
629 SCIP_EXPORT
631  SCIP* scip, /**< SCIP data structure */
632  SCIP_CONS* cons, /**< constraint data */
633  SCIP_EXPR* expr /**< new expression */
634  );
635 
636 /** adds coef * var to nonlinear constraint
637  *
638  * @attention This method can only be called in the problem stage.
639  */
640 SCIP_EXPORT
642  SCIP* scip, /**< SCIP data structure */
643  SCIP_CONS* cons, /**< constraint data */
644  SCIP_VAR* var, /**< variable */
645  SCIP_Real coef /**< coefficient */
646  );
647 
648 /** adds coef * expr to nonlinear constraint
649  *
650  * @attention This method can only be called in the problem stage.
651  */
652 SCIP_EXPORT
654  SCIP* scip, /**< SCIP data structure */
655  SCIP_CONS* cons, /**< nonlinear constraint */
656  SCIP_EXPR* expr, /**< expression */
657  SCIP_Real coef /**< coefficient */
658  );
659 
660 /** gets absolute violation of nonlinear constraint
661  *
662  * This function evaluates the constraints in the given solution.
663  *
664  * If this value is at most SCIPfeastol(), the constraint would be considered feasible.
665  */
666 SCIP_EXPORT
668  SCIP* scip, /**< SCIP data structure */
669  SCIP_CONS* cons, /**< constraint */
670  SCIP_SOL* sol, /**< solution to check */
671  SCIP_Real* viol /**< buffer to store computed violation */
672  );
673 
674 /** gets scaled violation of nonlinear constraint
675  *
676  * This function evaluates the constraints in the given solution.
677  *
678  * The scaling that is applied to the absolute violation of the constraint
679  * depends on the setting of parameter constraints/nonlinear/violscale.
680  */
681 SCIP_EXPORT
683  SCIP* scip, /**< SCIP data structure */
684  SCIP_CONS* cons, /**< constraint */
685  SCIP_SOL* sol, /**< solution to check */
686  SCIP_Real* viol /**< buffer to store computed violation */
687  );
688 
689 /** returns a variable that appears linearly that may be decreased without making any other constraint infeasible */
690 SCIP_EXPORT
692  SCIP* scip, /**< SCIP data structure */
693  SCIP_CONS* cons, /**< nonlinear constraint */
694  SCIP_VAR** var, /**< pointer to store the variable */
695  SCIP_Real* coef /**< pointer to store the coefficient */
696  );
697 
698 /** returns a variable that appears linearly that may be increased without making any other constraint infeasible */
699 SCIP_EXPORT
701  SCIP* scip, /**< SCIP data structure */
702  SCIP_CONS* cons, /**< nonlinear constraint */
703  SCIP_VAR** var, /**< pointer to store the variable */
704  SCIP_Real* coef /**< pointer to store the coefficient */
705  );
706 
707 
708 /* Methods for Expressions in Nonlinear Constraints
709  * All functions in this group assume that the expression is owned by a the nonlinear constraint handler.
710  */
711 
712 /** returns the number of positive rounding locks of an expression */
713 SCIP_EXPORT
715  SCIP_EXPR* expr /**< expression */
716  );
717 
718 /** returns the number of negative rounding locks of an expression */
719 SCIP_EXPORT
721  SCIP_EXPR* expr /**< expression */
722  );
723 
724 /** returns the variable used for linearizing a given expression (return value might be NULL)
725  *
726  * @note for variable expression it returns the corresponding variable
727  */
728 SCIP_EXPORT
730  SCIP_EXPR* expr /**< expression */
731  );
732 
733 /** returns the number of enforcements for an expression */
734 SCIP_EXPORT
736  SCIP_EXPR* expr /**< expression */
737  );
738 
739 /** returns the data for one of the enforcements of an expression */
740 SCIP_EXPORT
742  SCIP_EXPR* expr, /**< expression */
743  int idx, /**< position of enforcement in enfos array */
744  SCIP_NLHDLR** nlhdlr, /**< buffer to store nlhldr */
745  SCIP_NLHDLREXPRDATA** nlhdlrexprdata, /**< buffer to store nlhdlr data for expression, or NULL */
746  SCIP_NLHDLR_METHOD* nlhdlrparticipation, /**< buffer to store methods where nonlinear handler participates, or NULL */
747  SCIP_Bool* sepabelowusesactivity, /**< buffer to store whether sepabelow uses activity of some expression, or NULL */
748  SCIP_Bool* sepaaboveusesactivity, /**< buffer to store whether sepaabove uses activity of some expression, or NULL */
749  SCIP_Real* auxvalue /**< buffer to store current auxvalue, or NULL */
750  );
751 
752 /** sets the auxiliary value of expression for one of the enforcements of an expression */
753 SCIP_EXPORT
755  SCIP_EXPR* expr, /**< expression */
756  int idx, /**< position of enforcement in enfos array */
757  SCIP_Real auxvalue /**< the new value of auxval */
758  );
759 
760 /** number of nonlinear handlers whose activity computation and propagation methods depend on the activity of the expression
761  *
762  * @note This method can only be used after the detection methods of the nonlinear handlers have been called.
763  */
764 SCIP_EXPORT
766  SCIP_EXPR* expr /**< expression */
767  );
768 
769 /** number of nonlinear handlers whose separation methods (estimate or enforcement) depend on the activity of the expression
770  *
771  * @note This method can only be used after the detection methods of the nonlinear handlers have been called.
772  */
773 SCIP_EXPORT
775  SCIP_EXPR* expr /**< expression */
776  );
777 
778 /** number of nonlinear handlers whose separation methods (estimate or enforcement) use auxiliary variable of the expression
779  *
780  * @note This method can only be used after the detection methods of the nonlinear handlers have been called.
781  */
782 SCIP_EXPORT
784  SCIP_EXPR* expr /**< expression */
785  );
786 
787 /** method to be called by a nlhdlr during NLHDLRDETECT to notify an expression that it will be used
788  *
789  * - if `useauxvar` is enabled, then ensures that an auxiliary variable will be created in INITLP
790  * - if `useactivityforprop` or `useactivityforsepa{below,above}` is enabled, then ensured that activity will be updated for `expr`
791  * - if `useactivityforprop` is enabled, then increments the count returned by SCIPgetExprNPropUsesActivityNonlinear()
792  * - if `useactivityforsepa{below,above}` is enabled, then increments the count returned by SCIPgetExprNSepaUsesActivityNonlinear()
793  * and also increments this count for all variables in the expression.
794  *
795  * The distinction into `useactivityforprop` and `useactivityforsepa{below,above}` is to recognize variables which domain influences
796  * under/overestimators. Domain propagation routines (like OBBT) may invest more work for these variables.
797  * The distinction into `useactivityforsepabelow` and `useactivityforsepaabove` is to recognize whether a nlhdlr that called this method
798  * will use activity of `expr` in enfomethod \ref SCIP_NLHDLR_METHOD_SEPABELOW or \ref SCIP_NLHDLR_METHOD_SEPAABOVE.
799  */
800 SCIP_EXPORT
802  SCIP* scip, /**< SCIP data structure */
803  SCIP_EXPR* expr, /**< expression */
804  SCIP_Bool useauxvar, /**< whether an auxiliary variable will be used for estimate or cut generation */
805  SCIP_Bool useactivityforprop, /**< whether activity of expr will be used by domain propagation or activity calculation (inteval) */
806  SCIP_Bool useactivityforsepabelow, /**< whether activity of expr will be used by underestimation */
807  SCIP_Bool useactivityforsepaabove /**< whether activity of expr will be used by overestimation */
808  );
809 
810 /** computes absolute violation for auxvar relation in an expression w.r.t. original variables
811  *
812  * Assume the expression is f(x), where x are original (i.e., not auxiliary) variables.
813  * Assume that f(x) is associated with auxiliary variable z.
814  *
815  * If there are negative locks, then returns the violation of z &le; f(x) and sets `violover` to TRUE.
816  * If there are positive locks, then returns the violation of z &ge; f(x) and sets `violunder` to TRUE.
817  * Of course, if there both negative and positive locks, then return the violation of z = f(x).
818  *
819  * If necessary, f is evaluated in the given solution. If that fails (domain error),
820  * then `viol` is set to SCIPinfinity() and both `violover` and `violunder` are set to TRUE.
821  */
822 SCIP_EXPORT
824  SCIP* scip, /**< SCIP data structure */
825  SCIP_EXPR* expr, /**< expression */
826  SCIP_SOL* sol, /**< solution */
827  SCIP_Longint soltag, /**< tag of solution */
828  SCIP_Real* viol, /**< buffer to store computed violation */
829  SCIP_Bool* violunder, /**< buffer to store whether z >= f(x) is violated, or NULL */
830  SCIP_Bool* violover /**< buffer to store whether z <= f(x) is violated, or NULL */
831  );
832 
833 /** computes absolute violation for auxvar relation in an expression w.r.t. auxiliary variables
834  *
835  * Assume the expression is f(w), where w are auxiliary variables that were introduced by some nlhdlr.
836  * Assume that f(w) is associated with auxiliary variable z.
837  *
838  * If there are negative locks, then returns the violation of z &le; f(w) and sets `violover` to TRUE.
839  * If there are positive locks, then returns the violation of z &ge; f(w) and sets `violunder` to TRUE.
840  * Of course, if there both negative and positive locks, then return the violation of z = f(w).
841  *
842  * If the given value of f(w) is SCIP_INVALID, then `viol` is set to SCIPinfinity() and
843  * both `violover` and `violunder` are set to TRUE.
844  */
845 SCIP_EXPORT
847  SCIP* scip, /**< SCIP data structure */
848  SCIP_EXPR* expr, /**< expression */
849  SCIP_Real auxvalue, /**< the value of f(w) */
850  SCIP_SOL* sol, /**< solution that has been evaluated */
851  SCIP_Real* viol, /**< buffer to store computed violation */
852  SCIP_Bool* violunder, /**< buffer to store whether z >= f(w) is violated, or NULL */
853  SCIP_Bool* violover /**< buffer to store whether z <= f(w) is violated, or NULL */
854  );
855 
856 /** computes relative violation for auxvar relation in an expression w.r.t. auxiliary variables
857  *
858  * Assume the expression is f(w), where w are auxiliary variables that were introduced by some nlhdlr.
859  * Assume that f(w) is associated with auxiliary variable z.
860  *
861  * Taking the absolute violation from SCIPgetExprAbsAuxViolationNonlinear(), this function returns
862  * the absolute violation divided by max(1,|f(w)|).
863  *
864  * If the given value of f(w) is SCIP_INVALID, then `viol` is set to SCIPinfinity() and
865  * both `violover` and `violunder` are set to TRUE.
866  */
867 SCIP_EXPORT
869  SCIP* scip, /**< SCIP data structure */
870  SCIP_EXPR* expr, /**< expression */
871  SCIP_Real auxvalue, /**< the value of f(w) */
872  SCIP_SOL* sol, /**< solution that has been evaluated */
873  SCIP_Real* viol, /**< buffer to store computed violation */
874  SCIP_Bool* violunder, /**< buffer to store whether z >= f(w) is violated, or NULL */
875  SCIP_Bool* violover /**< buffer to store whether z <= f(w) is violated, or NULL */
876  );
877 
878 /** returns bounds on the expression
879  *
880  * This gives an intersection of bounds from
881  * - activity calculation (SCIPexprGetActivity()), if valid,
882  * - auxiliary variable, if present,
883  * - stored by SCIPtightenExprIntervalNonlinear() during domain propagation
884  *
885  * @note The returned interval can be empty!
886  */
887 SCIP_EXPORT
889  SCIP* scip, /**< SCIP data structure */
890  SCIP_EXPR* expr /**< expression */
891  );
892 
893 /** informs the expression about new bounds that can be used for reverse-propagation and to tighten bounds of
894  * corresponding (auxiliary) variable (if any)
895  *
896  * @attention this function should only be called during domain propagation in cons_nonlinear
897  */
898 SCIP_EXPORT
900  SCIP* scip, /**< SCIP data structure */
901  SCIP_EXPR* expr, /**< expression to be tightened */
902  SCIP_INTERVAL newbounds, /**< new bounds for the expression */
903  SCIP_Bool* cutoff, /**< buffer to store whether a cutoff was detected */
904  int* ntightenings /**< buffer to add the total number of tightenings, or NULL */
905  );
906 
907 /** mark constraints that include this expression to be propagated again
908  *
909  * This can be used by, e.g., nlhdlrs, to trigger a new propagation of constraints without
910  * a change of variable bounds, e.g., because new information on the expression is available
911  * that could potentially lead to tighter expression activity values.
912  *
913  * Note, that this call marks also constraints for propagation which only share some variable
914  * with this expression.
915  */
916 SCIP_EXPORT
918  SCIP* scip, /**< SCIP data structure */
919  SCIP_EXPR* expr /**< expression to propagate again */
920  );
921 
922 /** adds violation-branching score to an expression
923  *
924  * Adds a score to the expression-specific violation-branching score, thereby marking it as branching candidate.
925  * The expression must either be a variable expression or have an aux-variable.
926  * In the latter case, branching on auxiliary variables must have been enabled.
927  * In case of doubt, use SCIPaddExprsViolScoreNonlinear(). Roughly, the difference between these functions is that the current
928  * function adds `violscore` to the expression directly, while SCIPaddExprsViolScoreNonlinear() will split the
929  * violation score among all the given expressions according to parameter constraints/nonlinear/branching/violsplit.
930  *
931  * @see SCIPaddExprsViolScoreNonlinear()
932  */
933 SCIP_EXPORT
935  SCIP* scip, /**< SCIP data structure */
936  SCIP_EXPR* expr, /**< expression where to add branching score */
937  SCIP_Real violscore /**< violation score to add to expression */
938  );
939 
940 /** adds violation-branching score to a set of expressions, distributing the score among all the expressions
941  *
942  * Each expression must either be a variable expression or have an aux-variable.
943  * If branching on aux-variables is disabled, then the violation branching score will be distributed among all
944  * variables present in `exprs`.
945  */
946 SCIP_EXPORT
948  SCIP* scip, /**< SCIP data structure */
949  SCIP_EXPR** exprs, /**< expressions where to add branching score */
950  int nexprs, /**< number of expressions */
951  SCIP_Real violscore, /**< violation score to add to expression */
952  SCIP_SOL* sol, /**< current solution */
953  SCIP_Bool* success /**< buffer to store whether at least one violscore was added */
954  );
955 
956 /** gives violation-branching score stored in expression, or 0.0 if no valid score has been stored */
957 SCIP_EXPORT
959  SCIP_EXPR* expr /**< expression */
960  );
961 
962 /** returns the partial derivative of an expression w.r.t. a variable (or SCIP_INVALID if there was an evaluation error)
963  *
964  * @see SCIPexprGetDerivative()
965  */
966 SCIP_EXPORT
968  SCIP* scip, /**< SCIP data structure */
969  SCIP_EXPR* expr, /**< root expression of constraint used in the last SCIPevalExprGradient() call */
970  SCIP_VAR* var /**< variable (needs to be in the expression) */
971  );
972 
973 /** returns the var's coordinate of Hu partial derivative of an expression w.r.t. a variable (or SCIP_INVALID if there was an evaluation error)
974  *
975  * @see SCIPexprGetBardot()
976  */
977 SCIP_EXPORT
979  SCIP* scip, /**< SCIP data structure */
980  SCIP_EXPR* expr, /**< root expression of constraint used in the last SCIPevalExprHessianDir() call */
981  SCIP_VAR* var /**< variable (needs to be in the expression) */
982  );
983 
984 /** evaluates quadratic term in a solution w.r.t. auxiliary variables
985  *
986  * \note This requires that for every expr used in the quadratic data, a variable or auxiliary variable is available.
987  */
988 SCIP_EXPORT
990  SCIP* scip, /**< SCIP data structure */
991  SCIP_EXPR* expr, /**< quadratic expression */
992  SCIP_SOL* sol /**< solution to evaluate, or NULL for LP solution */
993  );
994 
995 /** @} */
996 /** @} */
997 
998 /**@addtogroup PublicNlhdlrInterfaceMethods
999  * @{
1000  */
1001 
1002 /** creates a nonlinear handler and includes it into the nonlinear constraint handler */
1003 SCIP_EXPORT
1005  SCIP* scip, /**< SCIP data structure */
1006  SCIP_NLHDLR** nlhdlr, /**< buffer where to store nonlinear handler */
1007  const char* name, /**< name of nonlinear handler (must not be NULL) */
1008  const char* desc, /**< description of nonlinear handler (can be NULL) */
1009  int detectpriority, /**< detection priority of nonlinear handler */
1010  int enfopriority, /**< enforcement priority of nonlinear handler */
1011  SCIP_DECL_NLHDLRDETECT((*detect)), /**< structure detection callback of nonlinear handler */
1012  SCIP_DECL_NLHDLREVALAUX((*evalaux)), /**< auxiliary evaluation callback of nonlinear handler */
1013  SCIP_NLHDLRDATA* nlhdlrdata /**< data of nonlinear handler (can be NULL) */
1014  );
1015 
1016 /** get number of nonlinear handler */
1017 SCIP_EXPORT
1019  SCIP_CONSHDLR* conshdlr /**< nonlinear constraint handler */
1020  );
1021 
1022 /** get nonlinear handlers */
1023 SCIP_EXPORT
1025  SCIP_CONSHDLR* conshdlr /**< nonlinear constraint handler */
1026  );
1027 /** returns a nonlinear handler of a given name (or NULL if not found) */
1028 SCIP_EXPORT
1030  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
1031  const char* name /**< name of nonlinear handler */
1032  );
1033 
1034 /** gives expression data that a given nonlinear handler stored in an expression
1035  *
1036  * Returns NULL if expr has not been detected by nlhdlr or nlhdlr did not store data.
1037  */
1038 SCIP_EXPORT
1040  SCIP_NLHDLR* nlhdlr, /**< nonlinear handler */
1041  SCIP_EXPR* expr /**< expression */
1042  );
1043 
1044 /** @} */
1045 
1046 #ifdef __cplusplus
1047 }
1048 #endif
1049 
1050 #endif
enum SCIP_Result SCIP_RESULT
Definition: type_result.h:61
SCIP_RETCODE SCIPcreateConsBasicSignpowerNonlinear(SCIP *scip, SCIP_CONS **cons, const char *name, SCIP_VAR *x, SCIP_VAR *z, SCIP_Real exponent, SCIP_Real xoffset, SCIP_Real zcoef, SCIP_Real lhs, SCIP_Real rhs)
void SCIPaddExprViolScoreNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_Real violscore)
SCIP_RETCODE SCIPinsertBilinearTermExistingNonlinear(SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_VAR *x, SCIP_VAR *y, SCIP_VAR *auxvar, int nlockspos, int nlocksneg)
SCIP_RETCODE SCIPincludeConsUpgradeNonlinear(SCIP *scip, SCIP_DECL_NONLINCONSUPGD((*nlconsupgd)), int priority, SCIP_Bool active, const char *conshdlrname)
unsigned int SCIPgetExprNAuxvarUsesNonlinear(SCIP_EXPR *expr)
SCIP_RETCODE SCIPchgExprNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_EXPR *expr)
SCIP_RETCODE SCIPgetRelViolationNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_SOL *sol, SCIP_Real *viol)
SCIP_Real SCIPgetRhsNonlinear(SCIP_CONS *cons)
SCIP_RETCODE SCIPregisterExprUsageNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_Bool useauxvar, SCIP_Bool useactivityforprop, SCIP_Bool useactivityforsepabelow, SCIP_Bool useactivityforsepaabove)
SCIP_Bool SCIPassumeConvexNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_RETCODE SCIPmarkExprPropagateNonlinear(SCIP *scip, SCIP_EXPR *expr)
int SCIPgetNBilinTermsNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_NLHDLREXPRDATA * SCIPgetNlhdlrExprDataNonlinear(SCIP_NLHDLR *nlhdlr, SCIP_EXPR *expr)
SCIP_RETCODE SCIPchgRhsNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_Real rhs)
SCIP_RETCODE SCIPgetNlRowNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_NLROW **nlrow)
enum SCIP_Retcode SCIP_RETCODE
Definition: type_retcode.h:63
SCIP_NLHDLR * SCIPfindNlhdlrNonlinear(SCIP_CONSHDLR *conshdlr, const char *name)
#define SCIP_DECL_NLHDLRDETECT(x)
Definition: type_nlhdlr.h:177
int SCIPgetBilinTermIdxNonlinear(SCIP_CONSHDLR *conshdlr, SCIP_VAR *x, SCIP_VAR *y)
static GRAPHNODE ** active
void SCIPincrementCurBoundsTagNonlinear(SCIP_CONSHDLR *conshdlr, SCIP_Bool boundrelax)
SCIP_EXPRCURV SCIPgetCurvatureNonlinear(SCIP_CONS *cons)
SCIP_VAR ** x
Definition: circlepacking.c:63
SCIP_HASHMAP * SCIPgetVarExprHashmapNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_RETCODE SCIPcreateConsBasicSOCNonlinear(SCIP *scip, SCIP_CONS **cons, const char *name, int nvars, SCIP_VAR **vars, SCIP_Real *coefs, SCIP_Real *offsets, SCIP_Real constant, SCIP_VAR *rhsvar, SCIP_Real rhscoeff, SCIP_Real rhsoffset)
SCIP_RETCODE SCIPgetAbsViolationNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_SOL *sol, SCIP_Real *viol)
type definitions related to nonlinear handlers of nonlinear constraints
SCIP_NLHDLR ** SCIPgetNlhdlrsNonlinear(SCIP_CONSHDLR *conshdlr)
#define SCIP_DECL_NONLINCONSUPGD(x)
SCIP_Real SCIPgetExprViolScoreNonlinear(SCIP_EXPR *expr)
SCIP_RETCODE SCIPcreateConsBasicQuadraticNonlinear(SCIP *scip, SCIP_CONS **cons, const char *name, int nlinvars, SCIP_VAR **linvars, SCIP_Real *lincoefs, int nquadterms, SCIP_VAR **quadvars1, SCIP_VAR **quadvars2, SCIP_Real *quadcoefs, SCIP_Real lhs, SCIP_Real rhs)
SCIP_RETCODE SCIPcomputeFacetVertexPolyhedralNonlinear(SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_Bool overestimate, SCIP_DECL_VERTEXPOLYFUN((*function)), void *fundata, SCIP_Real *xstar, SCIP_Real *box, int nallvars, SCIP_Real targetvalue, SCIP_Bool *success, SCIP_Real *facetcoefs, SCIP_Real *facetconstant)
int SCIPgetExprNEnfosNonlinear(SCIP_EXPR *expr)
#define SCIP_DECL_NLHDLREVALAUX(x)
Definition: type_nlhdlr.h:202
SCIP_RETCODE SCIPgetExprAbsOrigViolationNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_SOL *sol, SCIP_Longint soltag, SCIP_Real *viol, SCIP_Bool *violunder, SCIP_Bool *violover)
SCIP_RETCODE SCIPcollectBilinTermsNonlinear(SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_CONS **conss, int nconss)
SCIP_RETCODE SCIPincludeNlhdlrNonlinear(SCIP *scip, SCIP_NLHDLR **nlhdlr, const char *name, const char *desc, int detectpriority, int enfopriority, SCIP_DECL_NLHDLRDETECT((*detect)), SCIP_DECL_NLHDLREVALAUX((*evalaux)), SCIP_NLHDLRDATA *nlhdlrdata)
SCIP_RETCODE SCIPcreateConsBasicNonlinear(SCIP *scip, SCIP_CONS **cons, const char *name, SCIP_EXPR *expr, SCIP_Real lhs, SCIP_Real rhs)
SCIP_RETCODE SCIPcreateConsQuadraticNonlinear(SCIP *scip, SCIP_CONS **cons, const char *name, int nlinvars, SCIP_VAR **linvars, SCIP_Real *lincoefs, int nquadterms, SCIP_VAR **quadvars1, SCIP_VAR **quadvars2, SCIP_Real *quadcoefs, SCIP_Real lhs, SCIP_Real rhs, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool dynamic, SCIP_Bool removable)
SCIP_EXPR * SCIPgetExprNonlinear(SCIP_CONS *cons)
unsigned int SCIPgetExprNPropUsesActivityNonlinear(SCIP_EXPR *expr)
SCIP_CONSNONLINEAR_BILINTERM * SCIPgetBilinTermNonlinear(SCIP_CONSHDLR *conshdlr, SCIP_VAR *x, SCIP_VAR *y)
SCIP_RETCODE SCIPaddExprNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_EXPR *expr, SCIP_Real coef)
SCIP_Real SCIPgetExprPartialDiffGradientDirNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_VAR *var)
void SCIPgetExprEnfoDataNonlinear(SCIP_EXPR *expr, int idx, SCIP_NLHDLR **nlhdlr, SCIP_NLHDLREXPRDATA **nlhdlrexprdata, SCIP_NLHDLR_METHOD *nlhdlrparticipation, SCIP_Bool *sepabelowusesactivity, SCIP_Bool *sepaaboveusesactivity, SCIP_Real *auxvalue)
SCIP_RETCODE SCIPaddLinearVarNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_Real coef)
int SCIPgetExprNLocksNegNonlinear(SCIP_EXPR *expr)
SCIP_RETCODE SCIPcheckQuadraticNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_Bool *isquadratic)
SCIP_Real SCIPgetExprPartialDiffNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_VAR *var)
#define SCIP_Bool
Definition: def.h:93
SCIP_CONSNONLINEAR_BILINTERM * SCIPgetBilinTermsNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_EXPRCURV
Definition: type_expr.h:57
unsigned int SCIP_NLHDLR_METHOD
Definition: type_nlhdlr.h:57
SCIP_RETCODE SCIPchgLhsNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_Real lhs)
SCIP_Longint SCIPgetLastBoundRelaxTagNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_Real SCIPevalBilinAuxExprNonlinear(SCIP *scip, SCIP_VAR *x, SCIP_VAR *y, SCIP_CONSNONLINEAR_AUXEXPR *auxexpr, SCIP_SOL *sol)
SCIP_RETCODE SCIPtightenExprIntervalNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_INTERVAL newbounds, SCIP_Bool *cutoff, int *ntightenings)
int SCIPgetExprNLocksPosNonlinear(SCIP_EXPR *expr)
SCIP_RETCODE SCIPprocessRowprepNonlinear(SCIP *scip, SCIP_NLHDLR *nlhdlr, SCIP_CONS *cons, SCIP_EXPR *expr, SCIP_ROWPREP *rowprep, SCIP_Bool overestimate, SCIP_VAR *auxvar, SCIP_Real auxvalue, SCIP_Bool allowweakcuts, SCIP_Bool branchscoresuccess, SCIP_Bool inenforcement, SCIP_SOL *sol, SCIP_RESULT *result)
void SCIPgetLinvarMayDecreaseNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_VAR **var, SCIP_Real *coef)
SCIP_Longint SCIPgetCurBoundsTagNonlinear(SCIP_CONSHDLR *conshdlr)
#define SCIP_DECL_VERTEXPOLYFUN(f)
SCIP_RETCODE SCIPgetExprAbsAuxViolationNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_Real auxvalue, SCIP_SOL *sol, SCIP_Real *viol, SCIP_Bool *violunder, SCIP_Bool *violover)
int SCIPgetNNlhdlrsNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_RETCODE SCIPincludeConshdlrNonlinear(SCIP *scip)
SCIP_RETCODE SCIPaddExprsViolScoreNonlinear(SCIP *scip, SCIP_EXPR **exprs, int nexprs, SCIP_Real violscore, SCIP_SOL *sol, SCIP_Bool *success)
#define SCIP_Real
Definition: def.h:186
SCIP_VAR ** y
Definition: circlepacking.c:64
SCIP_RETCODE SCIPgetExprRelAuxViolationNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_Real auxvalue, SCIP_SOL *sol, SCIP_Real *viol, SCIP_Bool *violunder, SCIP_Bool *violover)
SCIP_RETCODE SCIPcreateConsNonlinear(SCIP *scip, SCIP_CONS **cons, const char *name, SCIP_EXPR *expr, SCIP_Real lhs, SCIP_Real rhs, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool dynamic, SCIP_Bool removable)
#define SCIP_Longint
Definition: def.h:171
struct SCIP_NlhdlrExprData SCIP_NLHDLREXPRDATA
Definition: type_nlhdlr.h:413
struct SCIP_NlhdlrData SCIP_NLHDLRDATA
Definition: type_nlhdlr.h:412
SCIP_RETCODE SCIPinsertBilinearTermImplicitNonlinear(SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_VAR *x, SCIP_VAR *y, SCIP_VAR *auxvar, SCIP_Real coefx, SCIP_Real coefy, SCIP_Real coefaux, SCIP_Real cst, SCIP_Bool overestimate)
void SCIPsetExprEnfoAuxValueNonlinear(SCIP_EXPR *expr, int idx, SCIP_Real auxvalue)
unsigned int SCIPgetExprNSepaUsesActivityNonlinear(SCIP_EXPR *expr)
SCIP_VAR * SCIPgetExprAuxVarNonlinear(SCIP_EXPR *expr)
SCIP_Real SCIPevalExprQuadraticAuxNonlinear(SCIP *scip, SCIP_EXPR *expr, SCIP_SOL *sol)
SCIP_INTERVAL SCIPgetExprBoundsNonlinear(SCIP *scip, SCIP_EXPR *expr)
SCIP_Real SCIPgetLhsNonlinear(SCIP_CONS *cons)
SCIP_CONSNONLINEAR_AUXEXPR ** exprs
SCIP callable library.
void SCIPgetLinvarMayIncreaseNonlinear(SCIP *scip, SCIP_CONS *cons, SCIP_VAR **var, SCIP_Real *coef)