English

A new elementary proof for M-stationarity under MPCC-GCQ for mathematical programs with complementarity constraints

Optimization and Control 2023-06-22 v4

Abstract

It is known in the literature that local minimizers of mathematical programs with complementarity constraints (MPCCs) are so-called M-stationary points, if a weak MPCC-tailored Guignard constraint qualification (called MPCC-GCQ) holds. In this paper we present a new elementary proof for this result. Our proof is significantly simpler than existing proofs and does not rely on deeper technical theory such as calculus rules for limiting normal cones. A crucial ingredient is a proof of a (to the best of our knowledge previously open) conjecture, which was formulated in a Diploma thesis by Schinabeck.

Cite

@article{arxiv.2011.04474,
  title  = {A new elementary proof for M-stationarity under MPCC-GCQ for mathematical programs with complementarity constraints},
  author = {Felix Harder},
  journal= {arXiv preprint arXiv:2011.04474},
  year   = {2023}
}

Comments

7 pages

R2 v1 2026-06-23T20:00:59.126Z