AI 中文总结
研究涉及凸集距离的乘积空间范数最小化问题，利用凸分析等工具建立对偶最优性条件，可构造解集，还研究了相关问题的最优性条件与解集描述，通过实例说明结果。
AI 中文摘要
本文研究了涉及到凸集距离的乘积空间范数最小化问题。利用凸分析和泛函分析的标准工具，我们建立了完整的对偶必要和充分最优性条件，并表明整个解集可以从给定解处最优性条件产生的对偶向量构造出来。因此，我们研究了费马 - 托里拆利问题、切比雪夫中心问题和p - 费马 - 托里拆利问题的广义版本的最优性条件和解集描述。并在适用时与现有结果进行了比较。给出了配备不同范数的有限维和无限维空间中的例子来说明结果。
英文摘要
The paper studies product-space norm minimisation problems involving distances to convex sets. Using standard tools from convex and functional analysis, we establish complete dual necessary and sufficient optimality conditions and show that the entire solution set can be constructed from the dual vectors arising from the optimality conditions at a given solution. As a consequence, we study optimality conditions and solution set descriptions for generalised versions of the Fermat-Torricelli problem, the Chebyshev centre problem, and the p-Fermat-Torricelli problem. Comparisons with existing results are provided whenever applicable. Examples in finite and infinite dimensional spaces equipped with different norms are presented to illustrate the results.
Comments25 pages
