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Relations Between Abs-Normal NLPs and MPCCs Part 1: Strong Constraint Qualifications

Lisa Hegerhorst-Schultchen (hegerhorst***at***ifam.uni-hannover.de)
Christian Kirches (c.kirches***at***tu-bs.de)
Marc Steinbach (mcs***at***ifam.uni-hannover.de)

Abstract: 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.

Keywords: Non-smooth NLPs, abs-normal form, MPCCs, linear independence and Mangasarian-Fromovitz type constraint qualifications, optimality conditions

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 07/22/2019
Entry Accepted: 07/22/2019
Entry Last Modified: 07/29/2020

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