哈达玛流形上带有切换约束的多目标半无限优化问题的最优条件和对偶性

IF 0.8 3区 数学 Q2 MATHEMATICS
Balendu Bhooshan Upadhyay, Arnav Ghosh
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引用次数: 0

摘要

本文在哈达玛流形的框架内讨论了某类带切换约束的多目标半无限编程问题(简称 MSIPSC)。我们为哈达玛流形环境下的 MSIPSC 引入了阿巴迪约束限定(简称 ACQ)。通过 ACQ,我们得出了 MSIPSC 弱帕累托效率的必要条件。此外,通过使用大地准凸和伪凸假设,还推导出了 MSIPSC 弱帕累托效率的充分条件。随后,提出了与原始问题 MSIPSC 相关的蒙德-韦尔型和沃尔夫型对偶模型,并建立了 MSIPSC 与相应对偶模型相关的若干对偶结果。在著名的哈达玛流形框架内,例如由所有对称正定矩阵组成的集合和波恩卡雷半平面,提供了几个非难例,以说明本文所推导结果的重要性。据我们所知,这是第一次在哈达玛流形的背景下研究 MSIPSC 的最优条件和对偶性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Optimality conditions and duality for multiobjective semi-infinite optimization problems with switching constraints on Hadamard manifolds

Optimality conditions and duality for multiobjective semi-infinite optimization problems with switching constraints on Hadamard manifolds

This paper deals with a certain class of multiobjective semi-infinite programming problems with switching constraints (in short, MSIPSC) in the framework of Hadamard manifolds. We introduce Abadie constraint qualification (in short, ACQ) for MSIPSC in the Hadamard manifold setting. Necessary criteria of weak Pareto efficiency for MSIPSC are derived by employing ACQ. Further, sufficient criteria of weak Pareto efficiency for MSIPSC are deduced by using geodesic quasiconvexity and pseudoconvexity assumptions. Subsequently, Mond–Weir type and Wolfe type dual models are formulated related to the primal problem MSIPSC, and thereafter, several duality results are established that relate MSIPSC and the corresponding dual models. Several non-trivial examples are furnished in the framework of well-known Hadamard manifolds, such as the set consisting of all symmetric positive definite matrices and the Poincaré half plane, to illustrate the importance of the results derived in this article. To the best of our knowledge, this is the first time that optimality conditions and duality results for MSIPSC have been studied in the setting of Hadamard manifolds.

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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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