cons_abspower.h File Reference

Detailed Description

Constraint handler for absolute power constraints $\textrm{lhs} \leq \textrm{sign}(x+a) |x+a|^n + c z \leq \textrm{rhs}$.

Author

Stefan Vigerske

Definition in file cons_abspower.h.

#include "scip/def.h"
#include "scip/type_cons.h"
#include "scip/type_nlp.h"
#include "scip/type_retcode.h"
#include "scip/type_scip.h"
#include "scip/type_sol.h"
#include "scip/type_var.h"

Go to the source code of this file.

Functions
SCIP_RETCODE	SCIPincludeConshdlrAbspower (SCIP *scip)
Absolute Power Constraints
This constraint handler handles constraints of the form $$\textrm{lhs} \leq \textrm{sign}(x+a) |x+a|^n + c z \leq \textrm{rhs}$$ for $n > 1.0$ a rational number, $a$ and $c$ arbitrary, and $x$ and $z$ variables. Note that $x$ can have $-a$ in the interior of its domain. Constraints are enforced by separation, domain propagation, and spatial branching. Cuts that separate on the convex hull of the graph of $\textrm{sign}(x+a) |x+a|^n$ are generated as long as they separate the relaxation solution. Otherwise, spatial branching on $x$ is applied. Further, domain propagation is implemented to propagate bound changes on $x$ onto $z$, and vice versa, and repropagation is implemented to allow for conflict analysis. During presolve, a pairwise comparison of absolute power constraints may allow to fix or aggregate some variables. See also Stefan Vigerske Decomposition of Multistage Stochastic Programs and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming PhD Thesis, Humboldt-University Berlin, 2012, submitted.
SCIP_RETCODE	SCIPcreateConsAbspower (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, 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_Bool stickingatnode)
SCIP_RETCODE	SCIPcreateConsBasicAbspower (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)
SCIP_RETCODE	SCIPgetNlRowAbspower (SCIP *scip, SCIP_CONS *cons, SCIP_NLROW **nlrow)
SCIP_VAR *	SCIPgetNonlinearVarAbspower (SCIP *scip, SCIP_CONS *cons)
SCIP_VAR *	SCIPgetLinearVarAbspower (SCIP *scip, SCIP_CONS *cons)
SCIP_Real	SCIPgetExponentAbspower (SCIP *scip, SCIP_CONS *cons)
SCIP_Real	SCIPgetOffsetAbspower (SCIP *scip, SCIP_CONS *cons)
SCIP_Real	SCIPgetCoefLinearAbspower (SCIP *scip, SCIP_CONS *cons)
SCIP_Real	SCIPgetLhsAbspower (SCIP *scip, SCIP_CONS *cons)
SCIP_Real	SCIPgetRhsAbspower (SCIP *scip, SCIP_CONS *cons)
SCIP_Real	SCIPgetViolationAbspower (SCIP *scip, SCIP_CONS *cons, SCIP_SOL *sol)