b-stationarity

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

    Convergence of a Penalty Method for Mathematical Programmingwith ComplementarityConstraints

  • Xinmin Hu
  • Daniel Ralph
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , ,

    We adapt the convergence analysis of smoothing (Fukushima and Pang) and regularization (Scholtes) methods to a penalty framework for mathematical programs with complementarity constraints (MPCCs), and show that the penalty framework shares similar convergence properties to these methods. Moreover, we give sufficient conditions for a sequence generated by the penalty framework to be attracted to … Read more