A majorized penalty approach to inverse linear second order cone programming problems

Shiyun Wang; Yong-Jin Liu; Yong Jiang

doi:10.3934/jimo.2014.10.965

Article Contents

2014, Volume 10, Issue 3: 965-976. Doi: 10.3934/jimo.2014.10.965

This issue Previous Article Quadratic optimization over one first-order cone Next Article A sample average approximation method based on a D-gap function for stochastic variational inequality problems

A majorized penalty approach to inverse linear second order cone programming problems

1.
School of Science, Shenyang Aerospace University, Shenyang, 110136

Received: September 30, 2012

Revised: June 30, 2013

Published: June 2014

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Abstract

This paper focuses on a type of inverse linear second order cone programming (LSOCP) problems which require us to adjust the parameters in both the objective function and the constraint set of a given LSOCP problem as little as possible so that a known feasible solution becomes optimal one. This inverse problem can be formulated as a linear second order cone complementarity constrained optimization problem and is difficult to solve due to the presence of second order cone complementarity constraint. To solve this difficult problem, we first partially penalize the inverse problem and then propose the majorization approach to the penalized problem by solving a sequence of convex optimization problems with quadratic objective function and simple second order cone constraints. Numerical results demonstrate the efficiency of our approach to inverse LSOCP problems.

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Mathematics Subject Classification: Primary: 49M30, 65K05; Secondary: 90C30.

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