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arXiv · 2011.04474

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

Felix Harder
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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.

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Felix Harder. 2020-11-09. A new elementary proof for M-stationarity under MPCC-GCQ for mathematical programs with complementarity constraints. https://doi.org/10.46298/jnsao-2021-6903

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