A Simple But Effective Canonical Dual Theory Unified Algorithm for Global Optimization
Abstract
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.
Cite
@article{arxiv.1105.2270,
title = {A Simple But Effective Canonical Dual Theory Unified Algorithm for Global Optimization},
author = {Jiapu Zhang},
journal= {arXiv preprint arXiv:1105.2270},
year = {2012}
}
Comments
This paper has been withdrawn by the author due to the Only reason that the author has no interest in any thing about CDT & its related affairs. The ideas (1) searching on the saddle surface and (2) using SeDuMi were kicked off from this paper and this paper also labeled all its citations very clearly