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Indexed by:期刊论文

Date of Publication:2011-05-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE

Volume:54

Issue:6

Page Number:1269-1286

ISSN No.:1674-7283

Key Words:smoothing Newton method; MPEC; QVI; optimality conditions

Abstract:We consider a class of mathematical programs governed by parameterized quasi-variational inequalities (QVI). The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a system of nonsmooth equations under the linear independence constraint qualification and the strict slackness condition. A set of second order sufficient conditions for the mathematical program with parameterized QVI constraints are proposed, which are demonstrated to be sufficient for the second order growth condition. The strongly BD-regularity for the nonsmooth system of equations at a solution point is demonstrated under the second order sufficient conditions. The smoothing Newton method in Qi-Sun-Zhou [2000] is employed to solve this nonsmooth system and the quadratic convergence is guaranteed by the strongly BD-regularity. Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this class of optimization problems.