Strongly geodesic preinvexity and Strongly Invariant η-Monotonicity on Riemannian Manifolds and its Application

IF 1.8 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Rairo-Operations Research Pub Date : 2023-02-06 DOI:10.1051/ro/2023123

Akhlad Iqbal, Askar Hussain, H. A. Bhat

引用次数: 0

Abstract

This paper introduces the concepts of strongly geodesic preinvexity, strongly $\eta$-invexity of order $m$, and strongly invariant $\eta$-monotonicity of order $m$ on Riemannian manifolds. Additionally, it discusses an important characterization of these functions under a condition, known as $\text{{\bf Condition C}}^{\dagger}$, defined by Barani \cite{Poury1}. The paper provides various non-trivial examples to support these definitions. Furthermore, it presents a significant characterization of strict $\eta$-minimizers (or $\eta$-minimizers) of order $m$ for multi-objective optimization problems and a solution to the vector variational-like inequality problem.

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黎曼流形的强测地线前变性和强不变η单调性及其应用

本文介绍了黎曼流形上的强测地线前不变性、强$\eta$ -阶不变性$m$和强$\eta$ -阶单调性$m$的概念。此外，它还讨论了在巴拉尼\cite{Poury1}定义的$\text{{\bf Condition C}}^{\dagger}$条件下这些函数的重要特征。本文提供了各种重要的例子来支持这些定义。进一步，给出了多目标优化问题的严格$\eta$ -minimizers(或$m$阶的$\eta$ -minimizers)的重要特征，并给出了类向量变分不等式问题的一个解。

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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来源期刊

Rairo-Operations Research 管理科学-运筹学与管理科学

CiteScore

3.60

自引率

22.20%

发文量

206

审稿时长

>12 weeks

期刊介绍： RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.