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Optimality conditions and optimization methods for quartic polynomial optimization

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  • Wu, Zhiyou
  • Tian, Jing
  • Quan, Jing
  • Ugon, Julien

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.

Suggested Citation

  • Wu, Zhiyou & Tian, Jing & Quan, Jing & Ugon, Julien, 2014. "Optimality conditions and optimization methods for quartic polynomial optimization," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 968-982.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:968-982
    DOI: 10.1016/j.amc.2014.01.074
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    References listed on IDEAS

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    1. Z. Wu & J. Tian & J. Ugon, 2015. "Global optimality conditions and optimization methods for polynomial programming problems," Journal of Global Optimization, Springer, vol. 62(4), pages 617-641, August.

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