A PERTURBATION APPROACH FOR AN INVERSE LINEAR SECOND-ORDER CONE PROGRAMMING

Indexed by:期刊论文

Journal:JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

Included Journals:SCIE、Scopus

Volume:9

Issue:1

Page Number:171-189

ISSN No.:1547-5816

Key Words:Inverse optimization; linear second-order cone programming; perturbation approach; damped Newton method

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 epsilon = 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.

Date of Publication:2013-01-01