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

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Lisa C. Hegerhorst-Schultchen
  • Christian Kirches
  • Marc C. Steinbach

Research Organisations

External Research Organisations

  • Technische Universität Braunschweig
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Details

Original languageEnglish
Article number6672
JournalJournal of Nonsmooth Analysis and Optimization
Volume2021
Issue number2
Publication statusPublished - 18 Feb 2021

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

    math.OC, 90C30, 90C33, 90C46

Cite this

Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications. / Hegerhorst-Schultchen, Lisa C.; Kirches, Christian; Steinbach, Marc C.
In: Journal of Nonsmooth Analysis and Optimization, Vol. 2021, No. 2, 6672, 18.02.2021.

Research output: Contribution to journal › Article › Research › peer review

Hegerhorst-Schultchen, LC, Kirches, C & Steinbach, MC 2021, 'Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications', Journal of Nonsmooth Analysis and Optimization, vol. 2021, no. 2, 6672. https://doi.org/10.46298/jnsao-2021-6672
Hegerhorst-Schultchen, L. C., Kirches, C., & Steinbach, M. C. (2021). Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications. Journal of Nonsmooth Analysis and Optimization, 2021(2), Article 6672. https://doi.org/10.46298/jnsao-2021-6672
Hegerhorst-Schultchen LC, Kirches C, Steinbach MC. Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications. Journal of Nonsmooth Analysis and Optimization. 2021 Feb 18;2021(2):6672. doi: 10.46298/jnsao-2021-6672
Hegerhorst-Schultchen, Lisa C. ; Kirches, Christian ; Steinbach, Marc C. / Relations between Abs-Normal NLPs and MPCCs. Part 1 : Strong Constraint Qualifications. In: Journal of Nonsmooth Analysis and Optimization. 2021 ; Vol. 2021, No. 2.
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