Characterizing global optimality for DC optimization problems under convex inequality constraints

Characterizations of global optimality are given for general difference convex (DC) optimization problems involving convex inequality constraints. These results are obtained in terms of a-subdifferentials of the objective and constraint functions and do not require any regularity condition. An extension of Farkas' lemma is obtained for inequality systems involving convex functions and is used to establish necessary and sufficient optimality conditions. As applications, optimality conditions are also given for weakly convex programming problems, convex maximization problems and for fractional programming problems.