Isolated calmness of solution mappings in convex semi-infinite optimization

This paper is concerned with isolated calmness of the solution mapping of a parameterized convex semi-infinite optimization problem subject to canonical perturbations. We provide a sufficient condition for isolated calmness of this mapping. This sufficient condition characterizes the strong uniqueness of minimizers, under the Slater constraint qualification. Moreover, on the assumption that the objective function and the constraints are linear, we show that this condition is also necessary for isolated calmness.This research was partially supported by Grants MTM2005-08572-C03 (01-02) (MEC, Spain, and FEDER, E.U.). The second author was supported by the National Science Foundation