On the relation between MPECs and optimization problems in abs-normal form
Lisa C. Hegerhorst-Schultchen, Christian Kirches, Marc Christian Steinbach · Optimization methods & software · 2019
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.