Title of Paper:A perturbation approach for a type of inverse linear programming problems

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Date of Publication:2011-01-01

Journal:INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Included Journals:SCIE

Volume:88

Issue:3

Page Number:508-516

ISSN No.:0020-7160

Key Words:inverse optimization; linear programming; perturbation approach; inexact Newton method; quadratic convergence

Abstract:We consider an inverse linear programming (LP) problem in which the parameters in both the objective function and the constraint set of a given LP problem need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a linear complementarity constrained minimization problem. With the help of the smoothed Fischer-Burmeister function, we propose a perturbation approach to solve the inverse problem and demonstrate its global convergence. An inexact Newton method is constructed to solve the perturbed problem and numerical results are reported to show the effectiveness of the approach.