Optimality conditions and optimization methods for quartic polynomial optimization

doi:10.1016/j.amc.2014.01.074

Optimality conditions and optimization methods for quartic polynomial optimization

2014-04-01

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DOI：10.1016/j.amc.2014.01.074

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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 e-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 c-strongly) local optimization method and an auxiliary function. Numerical examples show that our algorithms are efficient and stable. (C) 2014 Elsevier Inc. All rights reserved.

Keywords:

Quartic polynomial optimization problem

Necessary global optimality condition

Linear transformation

Local optimization method

Global optimization method

Optimality conditions and optimization methods for quartic polynomial optimization

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