We consider the problems of minimizing a DC function under a cone-convex constraint and a set constraint. By using the infimal convolution of the conjugate functions, we present a new constraint qualification which completely characterizes the Farkas-type lemma and the stable zero Lagrange duality gap property for DC conical programming problems in locally convex spaces.
D. H. Fang. "Stable Zero Lagrange Duality for DC Conic Programming." J. Appl. Math. 2012 1 - 17, 2012. https://doi.org/10.1155/2012/606457