Stationarity conditions and their reformulations for mathematical programs with vertical complementarity constraints (Q1762397)

The authors derive the M-stationarity conditions for the mathematical program with vertical complementarity constraints (MPVCC). They derive the Mordukhovich-type stationarity conditions for the MPVCC as a complement of the work of \textit{H. Scheel} and \textit{S. Scholtes} [Math. Oper. Res. 25, No. 1, 1--22 (2000; Zbl 1073.90557)]. In order to solve various popular stationarity systems for MPVCC, the systems are reformulated as nonlinear equations with simple constraints. These constrained equations are solved by a modified Levenberg-Marquardt method. It is also shown that the min-max-min problems and the problems with max-min constraints can be reformulated as MPVCC.