A Newton-Based Perturbation Method for a Robust Inverse Optimization Problem  

作　　者：Zhiqiang JIA Jian GU Xiantao XIAO 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology [2]School of Sciences,Dalian Ocean University

出　　处：《Journal of Mathematical Research with Applications》2016年第6期741-753,共13页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11571059);the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK30)

摘　　要：In this paper,we aim to solve an inverse robust optimization problem,in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal one.We formulate this inverse problem as a minimization problem with a linear equality constraint,a second-order cone complementarity constraint and a linear complementarity constraint.A perturbation approach is constructed to solve the inverse problem.An inexact Newton method with Armijo line search is applied to solve the perturbed problem.Finally,the numerical results are reported to show the effectiveness of the approach.In this paper,we aim to solve an inverse robust optimization problem,in which the parameters in both the objective function and the robust constraint set need to be adjusted as little as possible so that a known feasible solution becomes the optimal one.We formulate this inverse problem as a minimization problem with a linear equality constraint,a second-order cone complementarity constraint and a linear complementarity constraint.A perturbation approach is constructed to solve the inverse problem.An inexact Newton method with Armijo line search is applied to solve the perturbed problem.Finally,the numerical results are reported to show the effectiveness of the approach.

关 键 词：constraint inverse minimization formulate adjusted perturbation perturbed equality stopping conic 

分 类 号：O224[理学—运筹学与控制论]