Stationarity Conditions and Their Reformulations for Mathematical Programs with Vertical Complementarity Constraints

Yan-Chao Liang () and Gui-Hua Lin ()
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Yan-Chao Liang: Dalian University of Technology
Gui-Hua Lin: Dalian University of Technology

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 4, 54-70

Abstract: 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.

Keywords: Mathematical program with vertical complementarity constraints; Stationarity; Constrained equation; Levenberg–Marquardt method (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-9992-x

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