We choose a frame including convex andΦ-convex Programming. Moreover the theory may be applied to vectorial and integer valued problems because our maps are group valued maps. We characterize regularized maps by the mean of their epigraph; this allowed us to extend a regularized map which is defined on aΦ-convex subset to the whole space and to characterize support functions as in classical convex analysis (theorems 5,6,7). At last we generalize [4] by associating a penalty system to a group valued minimization problem (theorem 9).