基于半E-凸集值映优化问题的Kuhn-Tucker型最优性条件
Kuhn-Tucker Type Optimality Conditions Based on Semi-E-Convex Set-Valued Map Optimization Problem
DOI: 10.12677/aam.2025.145271, PDF,    国家自然科学基金支持
作者: 邹东易：重庆电力高等专科学校人文素质学院，重庆
关键词: E-凸集；半E-凸集值映射；弱有效解；最优性条件；E-Convex Set； Semi-E-Convex Set-Valued Maps； Weakly Efficient Solution； Optimality Conditions
摘要: 集值优化是优化理论中的一个重要课题，在经济、管理等领域有着广泛的应用。本文在集值映射的半E-凸性假设下，利用择一定理，建立了集值优化问题的Kuhn-Tucker型最优性充分和必要条件。本文获得的结果推广了文献中的一些已知结果。
Abstract: The set-valued optimization, which is widely applied in fields such as economics and management, is an important topic in optimization theory. In this paper, we will establish Kuhn-Tucker type optimality sufficient and necessary conditions for set-valued optimization problems under the assumption of semi-E-convexity of the set-valued map by using the alternative theorem. The results obtained in this paper extend some known results in the literature.
文章引用：邹东易. 基于半E-凸集值映优化问题的Kuhn-Tucker型最优性条件[J]. 应用数学进展, 2025, 14(5): 412-416. https://doi.org/10.12677/aam.2025.145271

参考文献

[1] Youness, E.A. (1999) E-Convex Sets, E-Convex Functions, and E-Convex Programming. Journal of Optimization Theory and Applications, 102, 439-450. [Google Scholar] [CrossRef] 
[2] Chen, X. (2002) Some Properties of Semi-E-Convex Functions. Journal of Mathematical Analysis and Applications, 275, 251-262. [Google Scholar] [CrossRef] 
[3] Zhou, Z., Yang, X. and Wan, X. (2017) The Semi-E Cone Convex Set-Valued Map and Its Applications. Optimization Letters, 12, 1329-1337. [Google Scholar] [CrossRef] 
[4] Megahed, A.E.A., Gomma, H.G., Youness, E.A. and El-Banna, A.H. (2013) Optimality Conditions of E-Convex Programming for an E-Differentiable Function. Journal of Inequalities and Applications, 2013, Article No. 246. [Google Scholar] [CrossRef] 
[5] Antczak, T. and Abdulaleem, N. (2019) E-Optimality Conditions and Wolfe E-Duality for E-Differentiable Vector Optimization Problems with Inequality and Equality Constraints. Journal of Nonlinear Sciences and Applications, 12, 745-764. [Google Scholar] [CrossRef] 
[6] Abdulaleem, N. (2022) V-E-Invexity in E-Differentiable Multiobjective Programming. Numerical Algebra, Control & Optimization, 12, 427-443. [Google Scholar] [CrossRef] 
[7] Jahn, J. (2011) Vector Optimization: Theory, Applications and Extensions. 2nd Edition, Springer.
[8] 邹东易. 线性空间中半E-凸集值优化问题的最优性条件[D]: [硕士学位论文]. 重庆: 重庆理工大学, 2023.
[9] Li, Z. (1999) The Optimality Conditions for Vector Optimization of Set-Valued Maps. Journal of Mathematical Analysis and Applications, 237, 413-424. [Google Scholar] [CrossRef] 

为你推荐