A smoothing Newton method for mathematical programs constrained by parameterized quasi-variational inequalities  

作　　者：WU Jia ZHANG LiWei 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

出　　处：《Science China Mathematics》2011年第6期1269-1286,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11071029);the Fundamental Research Funds for the Central Universities

摘　　要：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.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.

关 键 词：smoothing Newton method MPEC QVI optimality conditions 

分 类 号：O177.91[理学—数学] O221.2[理学—基础数学]