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

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.