Abstract
We consider the mathematical program with vertical complementarity constraints. We show that the min-max-min problems and the problems with max-min constraints can be reformulated as the above problem. As a complement of the work of Scheel and Scholtes in 2000, we derive the Mordukhovich-type stationarity conditions for the considered problem. We further reformulate various popular stationarity systems as nonlinear equations with simple constraints. A modified Levenberg–Marquardt method is employed to solve these constrained equations.
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