Optimization Online


Solving Linear Programs with Complementarity Constraints using Branch-and-Cut

Bin Yu (binyu610***at***gmail.com)
John E. Mitchell (mitchj***at***rpi.edu)
Jong-Shi Pang (jongship***at***usc.edu)

Abstract: 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.

Keywords: linear programs with complementarity constraints, MPECs, branch and cut

Category 1: Complementarity and Variational Inequalities

Category 2: Combinatorial Optimization (Branch and Cut Algorithms )

Citation: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180. October 28, 2016.

Download: [PDF]

Entry Submitted: 10/28/2016
Entry Accepted: 10/28/2016
Entry Last Modified: 02/08/2018

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society