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

TL;DR

This paper explores the fundamental properties of the generalized multi-source Weber problem and introduces an adaptive boosted DCA algorithm, demonstrating its effectiveness through comprehensive evaluation.

Contribution

It provides new theoretical insights into the problem's properties and applies an improved algorithm for solving both constrained and unconstrained versions.

Findings

Proved existence of global optimal solutions.

Demonstrated compactness of the solution set.

Showed the efficiency of the adaptive BDCA algorithm.

Abstract

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.