Reverse convex problems: an approach based on optimality conditions

where f ,g :Rn →R are convex continuous functions and S is a nonempty, convex compact in Rn. Such problems have many practical and theoretical applications in telecommunication, mechanics, engineering design, economics, and other fields (see [1, 2, 21], etc.) and have been studied actively over the last four decades (see, e.g., [9, 19] and their references). In addition to these direct applications, (RP) may appear as subproblems in more difficult nonconvex problems [5, 17, 20]. Also it is known that reverse convex problems and the well-known convex maximization (concave minimization) problems are dual to each other and the latter has an abundance of applications [12, 19]. In the literature, this problem is known as theminimization problemwith a “hole” [3], the reverse convex problem (see [7, 11], etc.), the problem over complements of convex sets [13], the canonical d.c. programming problem (see [8, 18], etc.), and anticonvex