Optimality conditions and optimization methods for quartic polynomial optimization

Zhiyou Wu, Jing Tian, Jing Quan and Julien Ugon

Applied Mathematics and Computation, 2014, vol. 232, issue C, 968-982

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.

Keywords: Quartic polynomial optimization problem; Necessary global optimality condition; Linear transformation; Local optimization method; Global optimization method (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:968-982

DOI: 10.1016/j.amc.2014.01.074

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