- Title
- On the triality theory for a quartic polynomial optimization problem
- Creator
- Gao, David; Wu, Changzhi
- Date
- 2012
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/56909
- Identifier
- vital:4538
- Identifier
-
https://doi.org/10.3934/jimo.2012.8.229
- Identifier
- ISSN:1547-5816
- Abstract
- This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality. Results show that the triality theory holds strongly in the tri-duality form for our problem if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Some numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the local minimum and local maximum.
- Relation
- Journal of Industrial and Management Optimization Vol. 8, no. 1 (2012), p. 229-242
- Rights
- American Institute of Mathematical Sciences
- Rights
- This metadata is freely available under a CCO license
- Subject
- Canonical duality; Counter-examples; Global optimization; Polynomial optimization; Triality
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