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On First and Second Order Optimality Conditions for Abs-Normal NLP

Lisa Hegerhorst-Schultchen(hegerhorst***at***ifam.uni-hannover.de)
Marc Steinbach(mcs***at***ifam.uni-hannover.de)

Abstract: Structured nonsmoothness is widely present in practical optimization. A particularly attractive class of nonsmooth problems, both from a theoretical and from an algorithmic perspective, are optimization problems in so-called abs-normal form as developed by Griewank and Walther. Here we generalize their theory for the unconstrained case to nonsmooth NLPs with equality and inequality constraints in abs-normal form, obtaining similar necessary and sufficient conditions of first and second order that are directly based on classical Karush-Kuhn-Tucker (KKT) theory for smooth NLPs. Several small examples illustrate the theoretical results. We also give some brief remarks on the intimate relationship of abs-normal NLPs with MPECs.

Keywords: Nonsmooth NLP, abs-normal form, linear independence kink qualification, first and second order necessary and sufficient conditions

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Insitute of Applied Mathematics Leibniz University Hannover Welfengarten 1 30167 Hannover March 2019

Download: [PDF]

Entry Submitted: 03/06/2019
Entry Accepted: 03/06/2019
Entry Last Modified: 03/06/2019

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