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.

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