On the relation between MPECs and optimization problems in abs-normal form

Research output: Contribution to journalArticleResearchpeer review

Authors

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

Research Organisations

External Research Organisations

  • Technische Universität Braunschweig
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Details

Original languageEnglish
Pages (from-to)560-575
Number of pages16
JournalOptimization Methods and Software
Volume35
Issue number3
Publication statusPublished - 22 Mar 2019

Abstract

We show that the problem of unconstrained minimization of a function in abs-normal form is equivalent to identifying a certain stationary point of a counterpart Mathematical Program with Equilibrium Constraints (MPEC). Hence, concepts introduced for the abs-normal forms turn out to be closely related to established concepts in the theory of MPECs. We give a number of proofs of equivalence or implication for the kink qualifications LIKQ and MFKQ. We also show that the counterpart MPEC always satisfies MPEC-ACQ. We then consider non-smooth nonlinear optimization problems (NLPs) where both the objective function and the constraints are presented in the abs-normal form. We show that this extended problem class also has a counterpart MPEC problem.

Keywords

    90C30, 90C33, 90C46, abs-normal form, constraint qualifications, MPECs, Non-smooth optimization, stationarity conditions

ASJC Scopus subject areas

Cite this

On the relation between MPECs and optimization problems in abs-normal form. / Hegerhorst-Schultchen, Lisa Christine; Kirches, C.; Steinbach, Marc C.
In: Optimization Methods and Software, Vol. 35, No. 3, 22.03.2019, p. 560-575.

Research output: Contribution to journalArticleResearchpeer review

Hegerhorst-Schultchen LC, Kirches C, Steinbach MC. On the relation between MPECs and optimization problems in abs-normal form. Optimization Methods and Software. 2019 Mar 22;35(3):560-575. doi: 10.1080/10556788.2019.1588268
Hegerhorst-Schultchen, Lisa Christine ; Kirches, C. ; Steinbach, Marc C. / On the relation between MPECs and optimization problems in abs-normal form. In: Optimization Methods and Software. 2019 ; Vol. 35, No. 3. pp. 560-575.
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