Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak 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 number6773
JournalJournal of Nonsmooth Analysis and Optimization
Volume2021
Issue number2
Publication statusPublished - 18 Feb 2021

Abstract

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

Keywords

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

Cite this

Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications. / Hegerhorst-Schultchen, Lisa C.; Kirches, Christian; Steinbach, Marc C.
In: Journal of Nonsmooth Analysis and Optimization, Vol. 2021, No. 2, 6773, 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 2: Weak Constraint Qualifications', Journal of Nonsmooth Analysis and Optimization, vol. 2021, no. 2, 6773. https://doi.org/10.46298/jnsao-2021-6673
Hegerhorst-Schultchen, L. C., Kirches, C., & Steinbach, M. C. (2021). Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications. Journal of Nonsmooth Analysis and Optimization, 2021(2), Article 6773. https://doi.org/10.46298/jnsao-2021-6673
Hegerhorst-Schultchen LC, Kirches C, Steinbach MC. Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications. Journal of Nonsmooth Analysis and Optimization. 2021 Feb 18;2021(2):6773. doi: 10.46298/jnsao-2021-6673
Hegerhorst-Schultchen, Lisa C. ; Kirches, Christian ; Steinbach, Marc C. / Relations between Abs-Normal NLPs and MPCCs. Part 2 : Weak Constraint Qualifications. In: Journal of Nonsmooth Analysis and Optimization. 2021 ; Vol. 2021, No. 2.
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