Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2011-007 (March 16, 2011)

A Branch-and-Bound Method for Absolute Value Programs
by Shota Yamanaka and Masao Fukushima

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In recent years, the absolute value equation (AVE) has attracted a growing attention. The absolute value program (AVP) is an extension of AVE, which contains absolute values of variables in its objective function and constraints. In this paper, we propose an algorithm for the AVP, which is based on the branch-and-bound method. In the branching procedure, we generate two subproblems by restricting the sign of a variable to be nonnegative or nonpositive. In the bounding procedure, we utilize the duality results for AVP. Furthermore, we carry out numerical experiments for nonconvex multi-facility location problems to show the effectiveness of the proposed algorithm.