ИСТИНА

We present the local sensitivity analysis for constrained optimization problems under the CQ-type condiions significantly weaker than those traditionally used in this context, or just without any CQ-type conditions. Our basic 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 or/and the upper bound on the rate of growth of the optimal value function. This analysis does not rely on any CQ. We demonstrate how the estimate of the distance to the feasible set of the perturbed problem can be obtained under the assumptions weaker than Robinson's CQ. Several applications of our sensitivity results are also presented. In particular, we suggest a very simple and efficient approach to deriving sharp error estimates for power penalization schemes under very mild assumptions. In order to do this, we show that the solutions of the unconstrained penalized problem can be treared as solutions of the artificial constrained optimization problem, which can be considered as a perturbation of the original problem. These estimates are applicable to mathematical programs with equilibrium constraints (MPECs), which are currently the subject of active research in optimization literature. Some other applications are concerned with sensitivity analysis and relaxation schemes for MPECs, the latter being among the most promising approaches to the numerical treatment of MPECs.