一类DC复合优化问题的Fenchel C-conjugate对偶理论

Fenchel C-conjugate dual theory for a class of DC composite optimization problems

在局部分离凸空间中,考虑无约束的DC复合优化问题.根据均匀凸(简称e-凸)函数在c-共轭框架下的Fenchel-Moreau定理,利用扰动方法建立了DC复合优化问题的Fenchel对偶问题.进一步,借助c-共轭函数的上图性质,给出了原问题与Fenchel对偶问题的零对偶间隙,弱对偶和强对偶成立的正则条件.

In the locally separated convex space,the unconstrained DC composite optimization problems is considered.According to the Fenchel-Moreau theorem of evenly convex(e-convex,in brief)function in the c-conjugate scheme,the Fenchel duality problem of DC composite optimization problem is established by perturbation method.Furthermore,by means of the properties of the epigraph of the c-conjugate function,the regularity conditions for the zero duality gap,the weak duality,and the strong duality of the primal problem and Fenchel duality problem are given.