Strongly Stable C-stationary Points for Mathematical Programs with Complementarity Constraints

J. Rückmann, D. Hernández Escobar

In this talk we consider the class of mathematical programs with complementarity constraints (MPCC). Under an appropriate constraint qualification of Mangasarian-Fromovitz type we present a topological and an equivalent algebraic characterization of a strongly stable C-stationary point of MPCC. Strong stability refers to the local uniqueness, existence and continuous dependence of a solution for each sufficiently small perturbed problem where perturbations up to second order are allowed. This concept of strong stability was originally introduced by Kojima for standard nonlinear optimization problems; here, its generalization to MPCC demands a sophisticated technique which takes the combinatorial properties of the solution set of MPCC into account.

Keywords: Mathematical programs with complementarity constraints strongly stable C-stationary points local uniqueness of solutions

M. J. Cánovas Cánovas, J. Camacho Moro, H. Gfrerer, J. Parra López

H. Gfrerer, J. Outrata

J. Parra López, J. Camacho Moro, M. J. Cánovas Cánovas, J. E. Martínez Legaz