The Existence and Stability of Generalized Multi-Source Weber Problems
arXiv:2607.27900
The paper investigates a generalized multi-source Weber problem with set-valued targets using minimal time functions, establishing existence of solutions, their qualitative properties, Lipschitz continuity, and stability of solution mappings under perturbations.
Abstract
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.