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Relations Between Abs-Normal NLPs and MPECs Under Weak 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 continues an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPECs. We continue our study of general NLPs with equality and inequality constraints in abs-normal form, and their relation to equivalent MPEC reformulations. We introduce Abadie's and Guignard's kink qualification and prove relations to ACQ and GCQ for MPEC reformulations. Due to non-uniqueness of a specific slack reformulation, suggested in [8], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. As we cannot show this for Guignard type we introduce branch formulations for abs-normal NLPs and MPECs. Then, equivalence of Abadie's and Guginard's constraint qualifications for all branch problems hold. Finally, we consider M-stationarity and B-stationarity concepts for abs-normal NLPs and prove corresponding first order optimality conditions.

Keywords: Non-smooth NLPs, abs-normal form, MPECs, Abadie and Guignard type constraint qualifications, optimality conditions

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

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Entry Submitted: 08/14/2019
Entry Accepted: 08/14/2019
Entry Last Modified: 08/14/2019

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