具有固定边心和函数边心的康托洛维奇问题的对偶性

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI:10.1134/S0016266324020023

Konstantin Afonin

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引用次数: 0

摘要

摘要本文致力于研究具有固定边心的线性 Kantorovich 问题中的对偶性。研究证明，对于完全正则空间上的一般下半连续成本函数，康托洛维奇对偶性成立。在考虑这个问题的过程中，我们提出并解决了连续线性函数用 Radon 度量表示的问题，条件是函数的原点由 Radon 度量给出。此外，我们还考虑了两个新的原点优化问题，并证明了它们的对偶性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Duality for the Kantorovich Problem with a Fixed Barycenter and Barycenters of Functionals

The paper is devoted to the study of duality in the linear Kantorovich problem with a fixed barycenter. It is proved that Kantorovich duality holds for general lower semicontinuous cost functions on completely regular spaces. In the course of considering this subject, the question of representation of a continuous linear functional by a Radon measure is raised and solved, provided that the barycenter of the functional is given by a Radon measure. In addition, we consider two new barycentric optimization problems and prove duality results for them.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.