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

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.