- Title
- Complete solutions and triality theory to a nonconvex optimization problem with double-well potential in Rn
- Creator
- Morales-Silva, Daniel; Gao, David
- Date
- 2013
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/63748
- Identifier
- vital:5753
- Identifier
- ISSN:2155-3289
- Abstract
- 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 ℝn, 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 so- lutions. The methods and results presented in this note pave the way towards the proof of the triality theory in general cases.
- Relation
- Numerical Algebra, Control and Optimization Vol. 3, no. 2 (2013), p. 271-282
- Rights
- Copyright American Institute of Mathematical Sciences
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Canonical duality theory; Double-well potential; Global optimization; Nonlinear algebraic equations; Perturbation; Triality
- Full Text
- Reviewed
- Hits: 1907
- Visitors: 1954
- Downloads: 126
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Accepted Version | 409 KB | Adobe Acrobat PDF | View Details Download |