Minimizing sequences in problems with d.c. constraints

Nonconvex optimization problems with a single inequality constraint given by the difference of two convex functions (i.e., by a d.c. function) are considered. Such problems may have many local solutions and stationary points that are far (in terms of, say, the value of the objective function) from a global solution. Necessary and sufficient conditions are proved for minimizing sequences in these problems. A global search strategy is proposed that is based on these conditions and uses classical methods of optimization. Its global convergence is proved.