二元凸复合与DC复合优化问题的最优性条件
Optimality Conditions for the Convex Composite Optimization and Composite Optimization of DC with Binary Variable
摘要: 利用变分分析相关结论,对二元凸复合优化问题和DC复合优化问题的最优解进行刻画,推广了前人的相关结论。
Abstract: Characterizations of optimal solutions of convex and DC of composite optimization problems are described based on advanced tools of variational analysis, which extend the corresponding results in the previous papers.
文章引用:肖程凤, 田超松. 二元凸复合与DC复合优化问题的最优性条件[J]. 应用数学进展, 2024, 13(4): 1746-1757. https://doi.org/10.12677/aam.2024.134165

参考文献

[1] Mordukhovich, B.S. and Nam, N.M. (2005) Variational Stability and Marginal Functions via Generalized Differentiation. Mathematics of Operations Research, 30, 800-816. [Google Scholar] [CrossRef
[2] Mordukhovich, B.S., Nam, N.M. and Yen, N.D. (2009) Subgradients of Marginal Functions in Parametric Mathematical Programming. Mathematical Programming, 116, 369-396. [Google Scholar] [CrossRef
[3] Cánovas, M.J., López, M.A., Mordukhovich, B.S. and Parra, J. (2010) Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions. SIAM Journal on Optimization, 20, 2788-2806. [Google Scholar] [CrossRef
[4] Fang, D.H. and Zhao, X.P. (2016) Optimality Conditions for Convex and DC Infniteoptimization Problems. Journal of Nonlinear and Convex Analysis, 17, 683-700.
[5] Dinh, N., Mordukhovich, B.S. and Nghia, T.T.A. (2010) Subdifferentials of Value Functions and Optimality Conditions for DC and Bilevel Infinite and Semi-Infinite Programs. Mathematical Programming, 123, 101-138. [Google Scholar] [CrossRef
[6] Fang, D.H., Liu, W.L. and Wen, C.F. (2016) Generalized Subdifferentials of the Value Function for Parametrized DC Optimization Problems. Journal of Nonlinear and Convex Analysis, 17, 639-654.
[7] Zalinescu, C. (2002) Convex Analysis in General Vector Spaces. World Scientific, New Jersey. [Google Scholar] [CrossRef
[8] Mordukhovich, B.S. (2006) Variational Analysis and Generalized Differentiation, I: Basic Theory. Springer-Verlag, Berlin. [Google Scholar] [CrossRef
[9] Fang, D.H. and Zhang, Y. (2020) Optimality Conditions and Total Dualities for Conicprogramming Involving Composite Function. Optimization, 69, 305-327. [Google Scholar] [CrossRef
[10] Dinh, N., Goberna, M.A., López, M.A. and Son, T.Q. (2007) New Farkas-Type Constraint Qualifications in Convex Infinite Programming. ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV), 13, 580-597. [Google Scholar] [CrossRef
[11] Mordukhovich, B.S., Nam, N.M. and Yen, N.D. (2006) Fréchet Subdifferential Calculus and Optimality Conditions in Nondifferentiable Programming. Optimization, 55, 685-708. [Google Scholar] [CrossRef