Title: Simulated annealing algorithm for absolute value equations

Authors: Hossein Moosaei; Hamed Jafari; Saeed Ketabchi

Addresses: Department of Mathematics, Faculty of Science, University of Bojnord, Bojnord, Iran ' Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran ' Department of Applied Mathematics, Faculty of Mathematical Sciences, The University of Guilan, P.O. Box 1914, Rasht, Iran

Abstract: The main goal of this paper is to compute the solution to the NP-hard absolute value equations (AVEs) Ax - |x| = b when the singular values of A exceed 1. First we show the AVE is equivalent to a bilinear programming problem and then we present a system tantamount to this problem. We use the simulated annealing (SA) algorithm to solve this system. Finally, several examples are given to illustrate the implementation and efficiency of the proposed method.

Keywords: linear complementarity problem; simulated annealing algorithm; singular values; absolute value equations; AVEs.

DOI: 10.1504/IJOR.2017.085965

International Journal of Operational Research, 2017 Vol.30 No.1, pp.142 - 150

Received: 28 Jul 2014
Accepted: 09 Apr 2015
Published online: 21 Aug 2017 *

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