完整晶格优化问题中新的最小元素定理和埃克兰德变分原理的新概括

IF 0.8 3区 数学 Q2 MATHEMATICS
Yousuke Araya, Wei-Shih Du
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引用次数: 0

摘要

在本文中,我们首先介绍了黑岩田中霞(Kuroiwa-Tanaka-Ha)和雅恩霞(Jahn-Ha)提出的 n 维欧几里得空间幂集上的一些集合关系类型。我们还提到了集合关系的新型取消律。其次,我们介绍了 Hamel 等人提出的 n 维欧几里得空间幂集上的完全格值问题。在完全格中应用非线性标量化技术,我们提出了完全格优化问题中的新型最小元素定理和广义埃克兰变分法原理。我们还提出了与完全网格优化问题中著名的高桥最小化定理相关的最小解存在定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A new minimal element theorem and new generalizations of Ekeland’s variational principle in complete lattice optimization problem

A new minimal element theorem and new generalizations of Ekeland’s variational principle in complete lattice optimization problem

In this paper, we first introduce some types of set relations on the power set of n-dimensional Euclidean spaces which are proposed by Kuroiwa–Tanaka–Ha and Jahn–Ha. We also mention new types of cancellation laws of set relations. Second, we introduce a complete lattice-valued problem on the power set of n-dimensional Euclidean spaces proposed by Hamel et al. Applying nonlinear scalarizing technique in complete lattice, we present a new type of minimal element theorem and generalized Ekeland’s variational principles in complete lattice optimization problem. We also present an existence theorem of minimal solutions related to the famous Takahashi’s minimization theorem in complete lattice optimization problem.

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来源期刊
Positivity
Positivity 数学-数学
CiteScore
1.80
自引率
10.00%
发文量
88
审稿时长
>12 weeks
期刊介绍: The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.
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