位置问题中的热带凸性

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Andrei Comăneci
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引用次数: 0

摘要

我们研究了在给定输入点的热带凸壳内找到最优解的定位问题。我们最初的研究重点是使用非对称热带距离的大地星凸集。我们引入了热带准凸函数的概念,它具有这种形状的子级集,与单调函数密切相关。我们的研究结果表明,使用热带准凸函数作为距离度量的定位问题,会在输入点的热带凸壳范围内得到最优解。我们还将这一结果扩展到输入点被替换为热带凸集的情况。最后,我们探讨了我们的研究在系统发育学中的应用,强调了由我们这一类定位问题产生的共识方法的特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Tropical convexity in location problems

Tropical convexity in location problems

We investigate location problems where the optimal solution is found within the tropical convex hull of the given input points. Our initial focus is on geodesically star-convex sets, using the asymmetric tropical distance. We introduce the concept of tropically quasiconvex functions, which have sub-level sets with this shape, and are closely related to monotonic functions. Our findings demonstrate that location problems using tropically quasiconvex functions as distance measures will result in an optimal solution within the tropical convex hull of the input points. We also extend this result to cases where the input points are replaced with tropically convex sets. Finally, we explore the applications of our research in phylogenetics, highlighting the properties of consensus methods that arise from our class of location problems.

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来源期刊
CiteScore
1.90
自引率
0.00%
发文量
36
审稿时长
>12 weeks
期刊介绍: This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.
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