presol_qpkktref.h
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30 * This presolver tries to add the KKT conditions as additional (redundant) constraints to the (mixed-binary) quadratic
40 * We first check if the structure of the program is like (QP), see the documentation of the function
43 * If the problem is known to be bounded (all variables have finite lower and upper bounds), then we add the KKT
53 * where \f$\mu\f$ are the Lagrangian variables. Each of the complementarity constraints \f$\mu_i \cdot (Ax - b)_i = 0\f$
54 * is enforced via an SOS1 constraint for \f$\mu_i\f$ and an additional slack variable \f$s_i = (Ax - b)_i\f$.
68 * where \f$J = \{1,\dots, p\}\f$, \f$\mu\f$ and \f$\lambda\f$ are the Lagrangian variables, and \f$I_J\f$ is the
69 * submatrix of the \f$n\times n\f$ identity matrix with columns indexed by \f$J\f$. For the derivation of the KKT-like
79 * - we handle the bilinear term variables of the quadratic constraint like in the method presolveAddKKTQuadBilinearTerms()
80 * - we handle the linear term variables of the quadratic constraint like in the method presolveAddKKTQuadLinearTerms()
84 * we have a hashmap from each variable to the index of the dual constraint in the KKT conditions.
87 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
Definition: struct_scip.h:68
SCIP_RETCODE SCIPincludePresolQPKKTref(SCIP *scip)
Definition: presol_qpkktref.c:2064
type definitions for return codes for SCIP methods
type definitions for SCIP's main datastructure
common defines and data types used in all packages of SCIP
Definition: objbenders.h:43