Kybernetika 35 no. 2, 177-193, 1999

Optimality conditions for a class of mathematical programs with equilibrium constraints: strongly regular case

Jiří V. Outrata


The paper deals with mathematical programs, where parameter-dependent nonlinear complementarity problems arise as side constraints. Using the generalized differential calculus for nonsmooth and set-valued mappings due to B. Mordukhovich, we compute the so-called coderivative of the map assigning the parameter the (set of) solutions to the respective complementarity problem. This enables, in particular, to derive useful 1st-order necessary optimality conditions, provided the complementarity problem is strongly regular at the solution.