Solving a Continuous Multifacility Location Problem by DC Algorithms
Research of this author was partly supported by the USA National Science Foundation (Directorate for Mathematical and Physical Sciences) [grant number DMS-1512846], [grant number DMS-1808978] and [grant number DMS-1716057], by the USA Air Force Office of Scientific Research [grant number #15RT04], and by Australian Research Council [grant number DP-190100555].
Optimization Methods & Software
The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility location problems under consideration come from their intrinsic discrete, nonconvex, and nondifferentiable nature. We provide a reformulation of these problems as those of continuous optimization and then develop a new DC type algorithm for their solutions involving Nesterov's smoothing. The proposed algorithm is computationally implemented via MATLAB numerical tests on both artificial and real data sets.
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Bajaj, A., Mordukhovich, B. S., Nam, N. M., & Tran, T. (2020). Solving a continuous multifacility location problem by DC algorithms. Optimization Methods and Software, 37(1), 338–360.