Jiapu Zhang. A Simple But Effective Canonical Dual Theory Unified Algorithm for Global Optimization

Natural Sciences / Physics / Mathematical Physics

Submitted on: May 13, 2012, 09:14:41

Description: Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems sometimes is very difficult. This paper presents a very simple but very effective canonical duality theory (CDT) unified global optimization algorithm. This algorithm has convergence is proved in this paper. More important, for this CDT-unified algorithm, numerous numerical computational results show that it is very powerful not only for solving low-dimensional but also for solving high-dimensional nonconvex/nonsmooth optimization problems, and the global optimal solutions can be easily and elegantly got with zero dual gap.

By the way, this paper points out two research directions for CDT algorithm de-signing. One direction is to solve the canonical dual problems and another direction is to solve differential nonlinear (quadratic) equations of the the prime-dual Gao-Strang complementary problems of CDT. The author reserves the copyrights of all his ideas in this document and will specially write a book to address these two directional CDT algorithms soon.

The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.

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