Lagrange-type duality in DC programming

We show a Lagrange-type duality theorem for a DC programming problem, which is a generalization of previous results by J.-E. Martيnez-Legaz, M. Volle [5] and Y. Fujiwara, D. Kuroiwa [1] when all constraint functions are real-valued. To the purpose, we decompose the DC programming problem into certain infinite convex programming problems.