mathematical programs with complementarity constraints

On the boundedness of multipliers in augmented Lagrangian methods for mathematical programs with complementarity constraints

  • Roberto Andreani
  • Mariana da Rosa
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization Tags , , ,

    In this paper, we present a theoretical analysis of augmented Lagrangian (AL) methods applied to mathematical programs with complementarity constraints (MPCCs). Our focus is on a variant that reformulates the complementarity constraints using slack variables, where these constraints are handled directly in the subproblems rather than being penalized. We introduce specialized constraint qualifications (CQs) of … Read more

    Regularizing Bilevel Nonlinear Programs by Lifting

  • Hans Georg Bock
  • Sven Leyffer
  • Kathrin Hatz
  • Johannes P. Schlöder
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , ,

    This paper considers a bilevel nonlinear program (NLP) whose lower-level problem satisfies a linear independence constraint qualification (LICQ) and a strong second-order condition (SSOC). One would expect the resulting mathematical program with complementarity constraints (MPCC), whose constraints are the first-order optimality conditions of the lower-level NLP, to satisfy an MPEC-LICQ. We provide an example which … Read more