A Normative Dual Method For Nonconvex Nonsmooth Optimization Problems With Box Constraints

In this paper, the optimization methods for solving nonconvex and nonsmooth optimization problems with the box constrained are studied. By use of a canonical duality theory, these di?cult problems can be converted equivalently into the canonical dual problems, which can be easily solved by the deterministic methods. It is shown that there is no any duality gap between the primal and dual problems and they share the same critical points. Both global and local extremality conditions can be identified by the triality dual theory. Examples are given to illustrate the superiority of this method.