arXiv subjects

Nguyen Thi Thu Van

Publications and source records attributed to Nguyen Thi Thu Van.

2 recordsLinked to original sources

arXiv2026

Moreau Envelope-Based Clustering for Generalized Multi-Source Weber Problem

In this paper, we propose an efficient algorithm for data clustering based on the Moreau envelope, which approximates nonsmooth and nonconvex components of the generalized multi-source Weber problem. The number of clusters is not fixed in advance and is determined automatically by progressively removing empty or redundant clusters. The smoothing induced by the Moreau envelope transforms the original problem into a structured optimization task that can be efficiently solved using first-order methods and simple matrix vector operations. Numerical experiments on synthetic and real datasets show that the proposed approach is fast, scalable, and competitive with existing methods in both clustering quality and computational efficiency.

math.OC↗

arXiv2024

Qualitative Analysis and Adaptive Boosted DCA for Generalized Multi-Source Weber Problems

This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge function. This includes proving the existence of global optimal solutions, demonstrating the compactness of the solution set, and establishing optimality conditions for these solutions. Second, we apply Nesterov's smoothing and the adaptive Boosted Difference of Convex functions Algorithm (BDCA) to solve both the unconstrained and constrained versions of the generalized multi-source Weber problems. These algorithms build upon the work presented in [6,19]. We conduct a comprehensive evaluation of the adaptive BDCA, comparing its performance to the method proposed in [19], and provide insights into its efficiency.

math.OC↗