Duality for minimization of the difference of two <inline-formula><tex-math id="M1">$ \Phi_c $</tex-math></inline-formula>-convex functions

This paper concerns an optimization problem with objectives given as the difference of two $ \Phi_c $-convex functions, where a set constraint and a conic constraint are involved. In the framework of $ c $-conjugacy, where $ c $ is a coupling function, we firstly construct the generalized Lagrange and Fenchel dual problems by using the perturbation approach. Then, we obtain complete characterizations of the strong duality for these two dual problems, respectively. As applications, we provide corresponding results for minimization of the difference of two evenly quasiconvex functions.