Sensitivity analysis of the value function for nonsmooth optimization problems

In this paper we present sensitivity analysis for a nonsmooth optimization problem with equality and inequality constraints. A necessary optimality condition, based on the convexificators, under the local error bound constraint qualification is derived. Then, we employ them to establish upper estimates for Fréchet and limiting subdifferentials of the value function. Furthermore, we present sufficient conditions for Lipschitzness of the value function at the point of interest. Also, some examples are provided to clarify our results.