Optimality Conditions and Duality for DC Programming in Locally Convex Spaces

摘要

Consider the DC programming problem (P_A)inf_(x∈X){f(x) - g(Ax)}, where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y, respectively, and A is a linear operator from X to Y. By using the properties of the epigraph of the conjugate functions, the optimality conditions and strong duality of (P_A) are obtained.