ncp

M-stationarity of Local Minimizers of MPCCs and Convergence of NCP-based Methods

  • Kexin Wang
  • Lorenz T. Biegler
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    This paper focuses on solving mathematical programs with complementarity constraints (MPCCs) without assuming MPCC-LICQ or lower level strict complementarity at a solution. We show that a local minimizer of an MPCC is “piecewise M-stationary” un- der MPCC-GCQ; furthermore, every weakly stationary point of an MPCC is B-stationary if MPCC-ACQ holds. For the Bounding Algorithm proposed … Read more

    Solving Multi-Leader-Follower Games

  • Sven Leyffer
  • Todd S. Munson
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , ,

    Multi-leader-follower games arise when modeling competition between two or more dominant firms and lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We examine a variety of nonlinear optimization and nonlinear complementarity formulations of EPECs. We distinguish two broad cases: problems where the leaders can cost-differentiate and problems with price-consistent followers. We … Read more