On the triality theory for a quartic polynomial optimization problem

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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