锥约束复合优化问题的Lagrange对偶

Study on the Lagrange Dualities for Composite Optimization Problems with Conical Constraints

利用共轭函数的上图性质,引入新的约束规范条件,等价刻画了带锥约束的复合优化问题与其Lagrange对偶问题之间的弱对偶,零对偶及强对偶,推广和改进了前人的相关结论.

In terms of the epigraph of conjugate functions, we give some new con- straint qualifications, which completely characterize the weak duality, the zero duality and the strong duality between the primal problem with its Lagrange dual problem. Our results of the present paper extend and improve the corresponding ones in the literature.