ADVANCES IN CANONICAL DUALITY THEORY WITH APPLICATIONS TO GLOBAL OPTIMIZATION

Canonical duality theory is a potentially powerful methodology, which can be used to solve a wide class of discrete and continuous global optimization problems. This paper presents a brief review and recent developments of this theory with applications to some well-know problems including polynomial minimization, mixed integer and fractional programming, nonconvex minimization with nonconvex quadratic constraints, etc. Results shown that under certain conditions, these dicult problems can be solved by deterministic methods within polynomial times, and the NP-hard problems can be transformed to a minimal stationary problem in dual space. Concluding remarks and open problems are presented in the end.

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