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On the Relation between MPECs and Optimization Problems in Abs-Normal Form

L C Hegerhorst-Schultchen (hegerhorst***at***ifam.uni-hannover.de)
C Kirches (c.kirches***at***tu-bs.de)
M C Steinbach (mcs***at***ifam.uni-hannover.de)

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 abs-normal form. We show that this extended problem class also has a counterpart MPEC problem.

Keywords: Non-smooth optimization, abs-normal form, MPECs, constraint qualifications, stationarity conditions

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Submitted to Optimization Methods and Software

Download: [PDF]

Entry Submitted: 06/25/2018
Entry Accepted: 06/25/2018
Entry Last Modified: 06/25/2018

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