equilibrium problems

A Heuristic for Complementarity Problems Using Difference of Convex Functions

  • Steven A. Gabriel
  • Dominic C. Flocco
  • Trine Krogh Boomsma
  • Miguel A. Lejeune
  • Martin Schmidt
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    We present a new difference of convex functions algorithm (DCA) for solving linear and nonlinear mixed complementarity problems (MCPs). The approach is based on the reformulation of bilinear complementarity constraints as difference of convex (DC) functions, more specifically, the difference of scalar, convex quadratic terms. This reformulation gives rise to a DC program, which is … Read more

    Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

  • Hande Benson
  • Arun Sen
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Game Theory Tags , , , ,

    In this paper we consider the question of solving equilibrium problems—formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPEC’s)—as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get around these difficulties, present an example … Read more