W. Geremew | Searcharxiv

arXiv2026

Solving Regularized Multifacility Location Problems with Unknown Number of Centers via Difference-of-Convex Optimization

In this paper, we develop optimization methods for a new model of multifacility location problems defined by a Minkowski gauge with Laplace-type regularization terms. The model is analyzed from both theoretical and numerical perspectives. In particular, we establish the existence of optimal solutions and study qualitative properties of global minimizers. By combining Nesterov's smoothing technique with recent advances in difference-of-convex optimization, following the pioneering work of P. D. Tao and L. T. H. An and others, we propose efficient numerical algorithms for minimizing the objective function of this model. As an application, our approach provides an effective method for determining the number of centers in gauge-based multifacility location and clustering problems. Our results extend and complement recent developments.

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arXiv2017

A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique

This paper continues our effort initiated in [9] to study Multicast Communication Networks, modeled as bilevel hierarchical clustering problems, by using mathematical optimization techniques. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost through the network. The fact that the cluster centers and the total center have to be among the given nodes makes this problem a discrete optimization problem. Our approach is to reformulate the discrete problem as a continuous one and to apply Nesterov smoothing approximation technique on the Minkowski gauges that are used as distance measures. This approach enables us to propose two implementable DCA-based algorithms for solving the problems. Numerical results and practical applications are provided to illustrate our approach.

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