A perturbation approach for an inverse linear second-order cone programming

Yi Zhang; Yong Jiang; Liwei Zhang; Jiangzhong Zhang

doi:10.3934/jimo.2013.9.171

Article Contents

2013, Volume 9, Issue 1: 171-189. Doi: 10.3934/jimo.2013.9.171

This issue Previous Article Proximal point algorithm for nonlinear complementarity problem based on the generalized Fischer-Burmeister merit function Next Article Threshold value of the penalty parameter in the minimization of $L_1$-penalized conditional value-at-risk

A perturbation approach for an inverse linear second-order cone programming

1.
Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai, 200237
2.
School of Science, Shenyang Aerospace University, Shenyang, 110136
3.
Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024
4.
Division of Science and Technology, Beijing Normal University-Hong Kong, Baptist University United International College, Zhuhai, 519085

Received: March 31, 2011

Revised: May 31, 2012

Published: December 2012

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Abstract

A type of inverse linear second-order cone programming problems is discussed, in which the parameters in both the objective function and the constraint set of a given linear second-order cone programming need to be adjusted as little as possible so that a known feasible solution becomes optimal. This inverse problem can be formulated as a minimization problem with second-order cone complementarity constraints. With the help of the smoothed Fischer-Burmeister function over second-order cones, we construct a smoothing approximation of the formulated problem whose feasible set and optimal solution set are demonstrated to be continuous and outer semicontinuous respectively at the perturbed parameter $\varepsilon=0$. A damped Newton method is employed 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 of the damped Newton method for solving the inverse linear second-order cone programming.

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Mathematics Subject Classification: Primary: 90C26, 90C33; Secondary: 49M15, 49M20.

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