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

Published: 2018/06/25

Constrained Nonlinear Optimization abs-normal form, constraint qualifications, mpec's, nonsmooth optimization, stationarity conditions Short URL: https://optimization-online.org/?p=15248

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.

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

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