Unified canonical duality methodology for global optimization

A unified methodology is presented for solving general global optimization problems. Based on the canonical dualitytriality theory, the nonconvex/nonsmooth/discrete problems from totally different systems are reformulated as a canonical min–max problem, which is equivalent to a monotone variational inequality problem over a convex cone. Therefore, a complementary-dual projection method is used for finding global optimal solutions deterministically. The main time cost of this algorithm is the canonical dual projection via a Semidefinitive Programming (SDP) method, which is needed only if the canonical dual solution is not feasible. Concrete applications are presented to three well-known challenging problems in integer programming, sensor localization, and radial basis neural networks. Computational results show that the canonical dual projection is needed mainly for those degenerated problems, i.e. the problems with multiple global minimizers. We also present new optimality conditions which show that the sequential canonical transformation is a powerful tool for solving high-order nonconvex problems in complex systems.