Upper Lipschitz behavior of solutions to perturbed C1,1 programs

We analyze the local upper Lipschitz behavior of critical points, stationary solutions and local minimizers to parametric C^1,1 programs. In particular, we derive a characterization of this property for the stationary solution set map without assuming the Mangasarian–Fromovitz CQ. Moreover, conditions which also ensure the persistence of solvability are given, and the special case of linear constraints is handled. The present paper makes its approach via contingent derivatives of the Kojima function associated with the given optimization problem.