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This paper presents a canonical d.c. (difference of canonical and convexfunctions) programming problem, which can be used to model general globaloptimization problems in complex systems. It shows that by using the canonicalduality theory, a large class of nonconvex minimization problems can beequivalently converted to a unified concave maximization problem over a convexdomain, which can be solved easily under certain conditions. Additionally, adetailed proof for triality theory is provided, which can be used to identifylocal extremal solutions. Applications are illustrated and open problems arepresented.

On modeling and global solutions for d.c. optimization problems by canonical duality theory