On Tikhonov’s Reciprocity Principle and Optimality Conditions in d.c. Optimization

The basic idea of the reciprocity principle of Tikhonov is to construct, from a given problem, a reciprocal problem that has the same solution set as the original problem and some special structure one can employ to investigate theoretical properties as well as to develop solution methods. In this note, we prove the reciprocity principle for a pair of nonconvex optimization problems, from which some optimality conditions for d.c. optimization can be derived immediately