On the relation between MPECs and optimization problems in abs-normal form. (3rd May 2020)

• Record Type: Journal Article
• Authors: Hegerhorst-Schultchen, L. C.; Kirches, C.; Steinbach, M. C.
• Is Part Of: Optimization methods and software. Volume 35:Number 3(2020)
• Page Start: 560
• Page End: 575
• Publication Date: 2020-05-03
• Subjects: Non-smooth optimization -- abs-normal form -- MPECs -- constraint qualifications -- stationarity conditions; 90C30 -- 90C33 -- 90C46; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1588268
• Languages: English
• ISSNs: 1055-6788

Abstract

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.