Stationarity Conditions and Their Reformulations for Mathematical Programs with Vertical Complementarity Constraints |
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Authors: | Yan-Chao Liang Gui-Hua Lin |
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Institution: | (1) School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China |
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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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