Complete Solutions and Triality Theory to a Nonconvex Optimization Problem with Double-Well Potential in R^n

Details Complete Solutions and Triality Theory to a Nonconvex Optimization Problem with Double-Well Potential in R^n Complete Solutions and Triality Theory to a Nonconvex Optimization Problem with Double-Well Potential in R^n

2011-10-03

arxiv.org/abs/1110.0285v1

Physics

Mathematical Physics

18 pages, 7 figures; J. Math. Analysis and Applications, 2011

Scientific paper

The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double-min duality is solved for a nonconvex optimization problem with double-well potential in $\real^n$, which leads to a complete set of analytical solutions. Also a convergency theorem is proved for linear perturbation canonical dual method, which can be used for solving global optimization problems with multiple solutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.

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