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A hybrid ODE-based method for unconstrained optimization problems

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  • Yi-gui Ou
  • Guan-shu Wang

Abstract

This paper presents a hybrid ODE-based method for unconstrained optimization problems, which combines the idea of IMPBOT with the subspace technique and a fixed step-length. The main characteristic of this method is that at each iteration, a lower dimensional system of linear equations is solved only once to obtain a trial step. Another is that when a trial step is not accepted, this proposed method uses minimization of a convex overestimation, thus avoiding performing a line search to compute a step-length. Under some reasonable assumptions, the method is proven to be globally convergent. Numerical results show the efficiency of this proposed method in practical computations, especially for solving small scale unconstrained optimization problems. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Yi-gui Ou & Guan-shu Wang, 2012. "A hybrid ODE-based method for unconstrained optimization problems," Computational Optimization and Applications, Springer, vol. 53(1), pages 249-270, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:249-270
    DOI: 10.1007/s10589-012-9455-1
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    References listed on IDEAS

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    1. X.-L. Luo & C. T. Kelley & L.-Z. Liao & H. W. Tam, 2009. "Combining Trust-Region Techniques and Rosenbrock Methods to Compute Stationary Points," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 265-286, February.
    2. Jie Sun & Jiapu Zhang, 2001. "Global Convergence of Conjugate Gradient Methods without Line Search," Annals of Operations Research, Springer, vol. 103(1), pages 161-173, March.
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    Cited by:

    1. Yulong Xu & Jian-an Fang & Wu Zhu & Xiaopeng Wang & Lingdong Zhao, 2015. "Differential evolution using a superior–inferior crossover scheme," Computational Optimization and Applications, Springer, vol. 61(1), pages 243-274, May.

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