AI 中文总结
本文在极小时间函数框架下研究带集值目标的广义多源韦伯问题，建立其最优解存在性、解集性质，推导函数的Lipschitz连续性，分析解映射的稳定性，为该问题提供敏感性分析。
AI 中文摘要
本文在极小时间函数框架下研究带集值目标的广义多源韦伯问题。首先建立全局与局部最优解的存在性，考察对应解集的若干定性性质，包括闭性、紧性，以及确保有界性或无界性的条件。接着推导目标函数与关联最优值函数关于目标集扰动的显式Lipschitz连续性性质。随后引入全局与局部解映射，从集值分析视角研究其稳定性性质。这些结果为极小时间函数框架下的广义多源韦伯问题提供了定量与定性的敏感性分析。
英文摘要
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.
