arXiv subjects

N. M. Nam

Publications and source records attributed to N. M. Nam.

6 recordsLinked to original sources

arXiv2026

Stability Analysis of Generalized Multi-Source Weber Problems

This paper presents a stability analysis of the generalized multi-source Weber problems under the influence of data perturbation within the framework of the Minkowski function. First, we establish explicit Lipschitz constants for the objective functions and optimal value functions. Then, we prove several properties of the global optimal solution sets. Furthermore, we provide sufficient conditions for the upper semicontinuity of global solution mappings and the inner semicontinuity of local solution mappings. Three illustrative examples are constructed. Our results give indirect answers to several open questions regarding the stability of local optimal solution mappings of the optimization problems discussed.

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arXiv2026

On the Strong Quasiconvexity of Norms and Distance Functions

This paper studies the strong quasiconvexity of norm and distance functions in finite-dimensional normed spaces. Although the Euclidean norm is known to be strongly quasiconvex on bounded convex sets, a complete characterization of this property for general norms remains open. We establish necessary and sufficient conditions for a norm function to be strongly quasiconvex on a convex set. We also initiate the study of the strong quasiconvexity of distance functions. Our results provide new insights into the geometric properties of norm and distance functions and extend several existing results in the literature.

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arXiv2026

The Existence and Stability of Generalized Multi-Source Weber Problems

This paper studies the generalized multi-source Weber problem with set-valued targets in the framework of minimal time functions. We first establish the existence of global and local optimal solutions and investigate several qualitative properties of the corresponding solution sets, including closedness, compactness, and conditions ensuring boundedness or unboundedness. Next, we derive explicit Lipschitz continuity properties for the objective function and the associated optimal value function with respect to perturbations of the target sets. We then introduce the global and local solution mappings and study their stability properties from the viewpoint of set-valued analysis. These results provide a quantitative and qualitative sensitivity analysis for the generalized multi-source Weber problem in the setting of minimal time functions.

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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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arXiv2025

Qualitative and Generalized Differentiation Properties of Optimal Value Functions with Applications to Duality

This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces are then established. We proceed by analyzing general properties of the optimal value function, including its domain, epigraph, strict epigraph, near convexity, semicontinuity, and Lipschitz-type continuity in both convex and nonconvex settings. Subsequently, we derive calculus rules and representation formulas for the $ε$-subdifferentials of the optimal value function and its Fenchel conjugate. We then develop a duality framework for constrained optimization problems with set-valued constraints using the Fenchel conjugate for set-valued mappings. This approach provides new perspectives on duality in generalized settings.

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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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