文献类型：期刊文献

英文题名：A PERTURBATION APPROACH FOR AN INVERSE QUADRATIC PROGRAMMING PROBLEM OVER SECOND-ORDER CONES

作者：Zhang, Yi[1];Zhang, Liwei[2];Wu, Jia[2];Zhang, Jianzhong[3]

机构：[1]E China Univ Sci & Technol, Sch Sci, Dept Math, Shanghai 200237, Peoples R China;[2]Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China;[3]Hong Kong Baptist Univ, Beijing Normal Univ, United Int Coll, Div Sci & Technol, Zhuhai 519085, Peoples R China

年份：2015

卷号：84

期号：291

起止页码：209

外文期刊名：MATHEMATICS OF COMPUTATION

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000351441400008)】；

基金：The first author was supported by the Fundamental Research Funds for the Central Universities under project no. 222201314037 and the China Postdoctoral Science Foundation funded project no. 2013M541479.The second author was supported by the National Natural Science Foundation of China under project nos. 11071029, 91130007 and 91330206.The third author was supported by the National Natural Science Foundation of China under project no. 11301049 and the China Postdoctoral Science Foundation funded project no. 2013M541217.

语种：英文

外文关键词：Inverse optimization; second-order cone quadratic programming; perturbation approach; smoothing Newton method

摘要：This paper is devoted to studying a type of inverse second-order cone quadratic programming problems, in which the parameters in both the objective function and the constraint set of a given second-order cone quadratic programming problem need to be adjusted as little as possible so that a known feasible solution becomes optimal. This inverse problem can be written as a minimization problem with second-order cone complementarity constraints and a positive semidefinite cone constraint. Applying the duality theory, we reformulate this problem as a linear second-order cone complementarity constrained optimization problem with a semismoothly differentiable objective function, which has fewer variables than the original one. A perturbed problem is proposed with the help of the projection operator over second-order cones, whose feasible set and optimal solution set are demonstrated to be continuous and outer semicontinuous, respectively, as the parameter decreases to zero. A smoothing Newton method is constructed to solve the perturbed problem and its global convergence and local quadratic convergence rate are shown. Finally, the numerical results are reported to show the effectiveness for the smoothing Newton method to solve the inverse second-order cone quadratic programming problem.