A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets

2014/04/21 by Nguyen Thai An, An, Nguyen Thai, Nguyen Mau Nam +3
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1404.5113

Abstract

We study a location problem that involves a weighted sum of distances to closed convex sets. As several of the weights might be negative, traditional solution methods of convex optimization are not applicable. After obtaining some existence theorems, we introduce a simple, but effective, algorithm for solving the problem. Our method is based on the Pham Dinh - Le Thi algorithm for d.c. programming and a generalized version of the Weiszfeld algorithm, which works well for convex location problems.

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