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

jnsao:6903 - Journal of Nonsmooth Analysis and Optimization, October 22, 2021, Volume 2 - https://doi.org/10.46298/jnsao-2021-6903
A new elementary proof for M-stationarity under MPCC-GCQ for mathematical programs with complementarity constraints

Authors: Felix Harder

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.


Volume: Volume 2
Section: Original research articles
Published on: October 22, 2021
Accepted on: October 20, 2021
Submitted on: November 13, 2020
Keywords: Mathematics - Optimization and Control,90C33 (Primary) 90C30 (Secondary)


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