一类凸复合函数的共轭和次微分及应用  

Conjugation and Subdifferential of a Class of Convex Composite Functions and Applications

作　　者：徐刚 何丹露 冯世强[1] XU Gang;HE Dan-lu;FENG Shi-qiang(School of Mathematics and Information,China West Normal University,Nanchong 637000,Sichuan,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637000

出　　处：《韶关学院学报》2022年第9期18-25,共8页Journal of Shaoguan University

基　　金：国家自然科学基金项目(11871059);四川省高校创新团队(16TD0019)。

摘　　要：在有限维欧氏空间中研究了一类凸复合函数的共轭和次微分.通过引入了线性算子,研究了带线性算子的凸复合函数的凸性、共轭和次微分.最后,将得到的结果应用到锥约束优化问题,给出了最优解的存在性条件.In this paper,we investigate the conjugation and subdifferential of a class of convex composite functions in finite dimensional Euclidean spaces. By introducing linear operators,we study the convexity,the conjugation and subdifferential of convex composite functions with linear operators. Finally,we apply the obtained results to the cone constraint optimization problems and obtain the existence conditions of the optimal solution.

关 键 词：凸分析 共轭 次微分 线性算子 复合 

分 类 号：O224[理学—运筹学与控制论]