Strongly stable C-stationary points for mathematical programs with complementarity constraints

• Published in: Mathematical programming Vol. 189; no. 1-2; pp. 339 - 377
• Main Authors: Hernández Escobar, Daniel, Rückmann, Jan-J.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Combinatorics; Full Length Paper; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Optimization; Perturbation; Stability; Theoretical; 90C31; Parametric optimization; Basic Lagrange vector; 49K40; 90C33; MPCC; C-stationary point; C-Mangasarian–Fromovitz constraint qualification; Strong stability; Algebraic characterization; 65K10
• ISSN: 0025-5610; 1436-4646; 1436-4646
• DOI: 10.1007/s10107-020-01553-7

In this paper 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 for 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; here, its generalization to MPCC demands a sophisticated technique which takes the disjunctive properties of the solution set of MPCC into account.