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Sensitivity Analysis for Cone-Constrained Optimization Problems Under the Relaxed Constraint Qualifications

Peoples Friendship University, Miklukho-Maklaya Str. 6, 117198 Moscow, Russia
Moscow State University, Faculty of Computational Mathematics and Cybernetics, Department of Operations Research, Leninskiye Gori, GSP-2, 119992 Moscow, Russia
arutun{at}orc.ru
izmaf{at}ccas.ru

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.

Key Words: sensitivity analysis; parametric optimization; cone-constrained problem; constraint qualification; abnormal point; sufficient optimality condition; mathematical program with complementarity constraints
History: Received: May 25, 2004; revision received: September 16, 2004;