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On first and second order optimality conditions for abs-Normal NLP

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Authors

  • Lisa Christine Hegerhorst-Schultchen
  • Marc C. Steinbach

Research Organisations

Details

Original languageEnglish
Pages (from-to)2629-2656
Number of pages28
JournalOPTIMIZATION
Volume69
Issue number12
Publication statusPublished - 13 Jun 2019

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

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

ASJC Scopus subject areas

Cite this

On first and second order optimality conditions for abs-Normal NLP. / Hegerhorst-Schultchen, Lisa Christine; Steinbach, Marc C.
In: OPTIMIZATION, Vol. 69, No. 12, 13.06.2019, p. 2629-2656.

Research output: Contribution to journalArticleResearchpeer review

Hegerhorst-Schultchen, LC & Steinbach, MC 2019, 'On first and second order optimality conditions for abs-Normal NLP', OPTIMIZATION, vol. 69, no. 12, pp. 2629-2656. https://doi.org/10.1080/02331934.2019.1626386
Hegerhorst-Schultchen LC, Steinbach MC. On first and second order optimality conditions for abs-Normal NLP. OPTIMIZATION. 2019 Jun 13;69(12):2629-2656. doi: 10.1080/02331934.2019.1626386
Hegerhorst-Schultchen, Lisa Christine ; Steinbach, Marc C. / On first and second order optimality conditions for abs-Normal NLP. In: OPTIMIZATION. 2019 ; Vol. 69, No. 12. pp. 2629-2656.
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