Hausdorff continuity of solution maps to equilibrium problems via the oriented distance function

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters Pub Date : 2024-02-27 DOI:10.1007/s11590-024-02098-w

Lam Quoc Anh, Nguyen Huu Danh, Pham Thanh Duoc

引用次数: 0

Abstract

This paper aims to study the stability in the sense of Hausdorff continuity of solution maps to equilibrium problems without assuming the solid condition of ordered cones. We first propose a generalized concavity of set-valued maps and discuss its relation with the existing concepts. Then, by using the above property and the continuity of the objective function, sufficient conditions for the Hausdorff continuity of solution maps to scalar equilibrium problems are established. Finally, we utilize the oriented distance function to obtain the Hausdorff continuity of solution maps to set-valued equilibrium problems via the corresponding results of the scalar equilibrium problems.

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通过定向距离函数实现平衡问题解映射的豪斯多夫连续性

本文旨在研究平衡问题解映射在豪斯多夫连续性意义上的稳定性，而不假定有序锥体的实体条件。我们首先提出了集值映射的广义凹性，并讨论了它与现有概念的关系。然后，利用上述性质和目标函数的连续性，建立了标量平衡问题解映射的豪斯多夫连续性的充分条件。最后，我们利用定向距离函数，通过标量均衡问题的相应结果，得到了集值均衡问题解映射的 Hausdorff 连续性。

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

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.