Solving linear programs with complementarity constraints using branch-and-cut. A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a modeling paradigm for a broad collection of problems, including bilevel programs, Stackelberg games, inverse quadratic programs, and problems involving equilibrium constraints. The presence of the complementarity constraints results in a nonconvex optimization problem. We develop a branch-and-cut algorithm to find a global optimum for this class of optimization problems, where we branch directly on complementarities. We develop branching rules and feasibility recovery procedures and demonstrate their computational effectiveness in a comparison with CPLEX. The implementation builds on CPLEX through the use of callback routines. The computational results show that our approach is a strong alternative to constructing an integer programming formulation using big-(M) terms to represent bounds for variables, with testing conducted on general LPCCs as well as on instances generated from bilevel programs with convex quadratic lower level problems.
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References in zbMATH (referenced in 4 articles , 1 standard article )
Showing results 1 to 4 of 4.
- Jara-Moroni, Francisco; Mitchell, John E.; Pang, Jong-Shi; Wächter, Andreas: An enhanced logical benders approach for linear programs with complementarity constraints (2020)
- Fomeni, Franklin Djeumou; Gabriel, Steven A.; Anjos, Miguel F.: An RLT approach for solving the binary-constrained mixed linear complementarity problem (2019)
- Yu, Bin; Mitchell, John E.; Pang, Jong-Shi: Solving linear programs with complementarity constraints using branch-and-cut (2019)
- Kanno, Yoshihiro: Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach (2018)