Elements of global search in the general d.c. optimization problem

In this paper, we consider an optimization problem whose objective function and equality and inequality constraints are determined by d.c. functions. Using the method of exact penalties, we reduce the original problem to a penalized problem without constraints, which is a d.c. minimization problem. For this problem, we apply the conditions of global optimality, which possess an algorithmic (constructive) property. These conditions are generalized to the case of minimizing sequences for the original and penalized problems. We propose a method for solving the auxiliary problem based on optimality conditions. A global search scheme for solving the auxiliary and original problems is constructed and its convergence is proved.