Sensitivity analysis for cone-constrained optimization problems under the relaxed constraint qualifications

We present the local sensitivity analysis for cone-constrained optimization problems under the CQ-type conditions significantly weaker than those traditionally used in this context. Our basic sensitivity results are established under the first- or second-order sufficient optimality conditions combined with the estimate of the distance to the feasible set of the perturbed problem. We demonstrate how such an estimate can be obtained under the assumptions weaker than Robinson's CQ, and establish the corresponding sensitivity results. Finally, we apply our results to sensitivity analysis and relaxation schemes for mathematical programs with complementarity constraints.