mpccs

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) by assuming neither MPCC linear independence constraint qualification (MPCC-LICQ) nor lower/upper level strict complementarity at the solution. First, necessary conditions for MPCC local optimality and sufficient conditions for convergence to B-stationarity are investigated. Under MPCC-Abadie constraint qualification (MPCC-ACQ), we show that a local minimizer … Read more

    Relations Between Abs-Normal NLPs and MPCCs Part 2: Weak Constraint Qualifications

  • Lisa Hegerhorst-Schultchen
  • Christian Kirches
  • Marc C. Steinbach
    • Categories Nonsmooth Optimization Tags , , , ,

    This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie’s and Guignard’s kink qualification and … Read more

    Relations Between Abs-Normal NLPs and MPCCs Part 1: Strong Constraint Qualifications

  • Lisa Hegerhorst-Schultchen
  • Christian Kirches
  • Marc C. Steinbach
    • Categories Nonsmooth Optimization Tags , , , ,

    This work is part of an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general abs-normal NLP with equality and inequality constraints in relation to an equivalent MPCC reformulation. We show that kink qualifications and MPCC constraint qualifications of linear independence type and Mangasarian-Fromovitz type are equivalent. Then … Read more