On a Global Search in D.C. Optimization Problems

Abstract

This paper addresses the nonconvex optimization problem with the cost function and equality and inequality constraints given by d.c. functions. The original problem is reduced to a problem without constraints by means of the exact penalization techniques. Furthermore, the penalized problem is presented as a d.c. minimization problem. For the latter problem, we apply the global optimality conditions (GOCs), which possess the so-called constructive (algorithmic) property. These new GOCs are generalized for the minimizing sequences, and a theoretical method is developed. Based on this theoretical foundation, a new global search scheme is designed for the auxiliary (penalized) and original problems, the convergence of which is one of the new results of the work.