This paper presents a canonical duality theory for general box constrained nonconvex and nonsmooth optimization problems. The theory is illustrated perfectly by showing mainly a canonical dual transformation and a triality theory. It is proved that the general box constrained nonconvex and nonsmooth optimization problems can be changed into the perfect dual problems, which can be solved easily. The perfect dual transformation is developed for eliminating the duality gap,while the triality theorem studies global and local extreme conditions. Applications and examples are illustrated.
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