Lisa C. Hegerhorst-Schultchen ; Christian Kirches ; Marc C. Steinbach - Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications

jnsao:6672 - Journal of Nonsmooth Analysis and Optimization, February 18, 2021, Volume 2 - https://doi.org/10.46298/jnsao-2021-6672
Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications

Authors: Lisa C. Hegerhorst-Schultchen ; Christian Kirches ; Marc C. Steinbach

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 we consider strong stationarity concepts with first and second order optimality conditions, which again turn out to be equivalent for the two problem classes. Throughout we also consider specific slack reformulations suggested in [9], which preserve constraint qualifications of linear independence type but not of Mangasarian-Fromovitz type.


Volume: Volume 2
Section: Original research articles
Published on: February 18, 2021
Submitted on: July 30, 2020
Keywords: Mathematics - Optimization and Control,90C30, 90C33, 90C46


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