Semi‐Infinite Optimization under Convex Function Perturbations: Lipschitz Stability

This paper is devoted to the study of the stability of the solution map for the parametric convex semi‐infinite optimization problem under convex function perturbations in short, PCSI. We establish sufficient conditions for the pseudo‐Lipschitz property of the solution map of PCSI under perturbations of both objective function and constraint set. The main result obtained is new even when the problems under consideration reduce to linear semi‐infinite optimization. Examples are given to illustrate the obtained results.