广义共轭框架下约束复合优化的逆对偶

Converse Duality for Constrained Composed Optimization via a Generalized Conjugation Scheme

在可分离局部凸拓扑空间上,主要研究目标函数带有连续线性映射复合的约束优化问题.借助c-共轭模式和扰动法,得到了该约束复合优化的3个对偶问题,并且结合扰动函数的均匀凸性,具体给出了逆对偶成立的充分条件.

In separated locally convex topological spaces,the general constrained optimization problem owing the composition with a linear continuous mapping in the objective function is mainly studies.By means of a coupling conjugation scheme and the perturbational approach,three dual problems of the constrained composed optimization are obtained,and sufficient conditions for converse duality involving the even convexity of the perturbation function are specifically given.