拟凸优化问题严格解的最优性必要条件
Necessary Optimality Conditions of Strict Solutions for Quasiconvex Optimization Problems
DOI: 10.12677/AAM.2019.83045, PDF,    国家自然科学基金支持
作者: 李林廷, 杨 铭, 高 英：重庆师范大学数学科学学院，重庆
关键词: 拟凸优化；严格解；最优性条件；Quasiconvex Optimization Problems； Strict Solution； Optimality Condition
摘要: 本文对拟凸多目标优化问题的严格解进行研究。利用拟凸次微分给出拟凸优化问题严格解的最优性必要条件。首先，引进拟凸函数次微分的基本概念和严格解的概念。然后，将拟凸函数次微分的概念应用到拟凸优化问题中，给出拟凸优化问题严格解的最优性必要条件。
Abstract: In this paper, we study the necessary conditions of strict solutions for quasiconvex optimization problems by using the subdifferential of quasiconvex function. Firstly, we introduce the basic concepts of quasiconvex optimization problem. Then, we derive the necessary conditions of the strict solutions for quasiconvex optimization problems.
文章引用：李林廷, 杨铭, 高英. 拟凸优化问题严格解的最优性必要条件[J]. 应用数学进展, 2019, 8(3): 400-406. https://doi.org/10.12677/AAM.2019.83045

参考文献

[1] Mangasarian, O.L. (1965) Pseudo Functions. Journal of the Society for Industrial and Applied Mathematics, 3, 23-32.
[2] Cottle, R.W. and Ferland, J.A. (1972) Matrix-Theoretic Criteria for the Quasi-Convexity and Pseu-do-Convexity of Quadratic Functions. Linear Algebra and Its Applications, 5, 123-136. [Google Scholar] [CrossRef] 
[3] Ferland, J.A. (1972) Mathematical Programming Problems with Quasi-Convex Objective Functions. Mathematical Programming, 3, 296-301. [Google Scholar] [CrossRef] 
[4] Greenberg, H.J. and Pierskalla, W.P. (1973) Quasi-Conjugate Functions and Surrogate Duality. Cahiers du Centre d’Etudes de Recherche Operationelle, 15, 437-448.
[5] Plastria, F. (1985) Lower Subdifferentiable Functions and Their Minization by Cutting Planes. Journal of Optimization Theory and Applications, 46, 37-53. [Google Scholar] [CrossRef] 
[6] Penot, J.P. (1998) Are Generalized Derivatives Useful for Generalized Convex Functions Generalized Convexity, Generalized Monotonicity: Recent Results. Springer, 3-59. [Google Scholar] [CrossRef] 
[7] Penot, J.P. (2000) What Is Quasiconvex Analysis. Optimization, 47, 35-110. [Google Scholar] [CrossRef] 
[8] Nguyen, T.H.L and Penot, J.P. (2006) Optimality Conditions for Quasiconvex Programs. SIAM Journal on Optimization, 17, 500-510. [Google Scholar] [CrossRef] 
[9] Gao, Y., Yang, X.M. and Lee, H.W.J. (2010) Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems. Journal of Inequalities and Applications, 2010, 620-928. [Google Scholar] [CrossRef] 
[10] Suzuki, S. and Kuroiwa, D. (2011) Optimality Conditions and the Basic Constraint Qualification for Quasiconvex Programming. Nonlinear Analysis, 74, 1279-1285. [Google Scholar] [CrossRef] 
[11] Khanh, P.Q., Quyen, H.T. and Yao, J.C. (2011) Optimality Condi-tions under Relaxed Quasiconvexity Assumptions Using Star and Adjusted Subdifferentials. European Journal of Op-erational Research, 212, 235-241. [Google Scholar] [CrossRef] 
[12] 陈瑞婷, 徐智会, 高英. 拟凸多目标优化问题近似解的最优性条件[J]. 运筹学学报(已接收).
[13] Durea, M. (2010) Remark on Strict Efficiency in Scalar and Vector Optimization. Journal of Global Optimization, 47, 13-27. [Google Scholar] [CrossRef] 
[14] 林锉云, 董家礼. 多目标最优化的方法和理论[M]. 长春: 吉林教育出版社, 1992..
[15] 谢静. 向量优化问题的最优性条件研究[D]: [硕士学位论文]. 重庆: 重庆师范大学, 2018.

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