- Title
- Optimality conditions and optimization methods for quartic polynomial optimization
- Creator
- Wu, Zhiyou; Tian, Jing; Quan, Jing; Ugon, Julien
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/168983
- Identifier
- vital:13929
- Identifier
-
https://doi.org/10.1016/j.amc.2014.01.074
- Identifier
- ISBN:0096-3003
- Abstract
- In this paper multivariate quartic polynomial optimization program (QPOP) is considered. Quartic optimization problems arise in various practical applications and are proved to be NP hard. We discuss necessary global optimality conditions for quartic problem (QPOP). And then we present a new (strongly or ε-strongly) local optimization method according to necessary global optimality conditions, which may escape and improve some KKT points. Finally we design a global optimization method for problem (QPOP) by combining the new (strongly or ε-strongly) local optimization method and an auxiliary function. Numerical examples show that our algorithms are efficient and stable.
- Publisher
- Elsevier
- Relation
- Applied Mathematics and Computation Vol. 232, no. (2014), p. 968-982
- Rights
- Copyright Elsevier
- Rights
- This metadata is freely available under a CCO license
- Subject
- Quartic polynomial optimization problem; Necessary global optimality condition; Linear transformation; Local optimization method; Global optimization method; 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0801 Artificial Intelligence and Image Processing
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