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Cross-Hill: A heuristic method for global optimization

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  • Wu, Tingting
  • Han, Deren
  • Xu, Yi

Abstract

The heuristic Cross-Hill method proposed by Qi et al. (2009) [14] was recently extended from finding the Z-eigenvalues of tensors to quantum separation problem by Han and Qi (2013) [5]. In this paper, we show that it can be extended to solve general global optimization problems. The heuristic Cross-Hill method is a combination of a local optimization method and a global optimization method with lower dimension. At each iteration, it first uses the local optimization method to find a local solution. Then, using this point and an arbitrary orthogonal vector, it solves a two-dimensional optimization problem to find a better solution than that the local approach was able to find. Preliminary experimental results are very encouraging.

Suggested Citation

  • Wu, Tingting & Han, Deren & Xu, Yi, 2015. "Cross-Hill: A heuristic method for global optimization," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 959-967.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:959-967
    DOI: 10.1016/j.amc.2015.06.013
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    Cited by:

    1. Wu, Tingting & Shao, Jinbo & Gu, Xiaoyu & Ng, Michael K. & Zeng, Tieyong, 2021. "Two-stage image segmentation based on nonconvex ℓ2−ℓp approximation and thresholding," Applied Mathematics and Computation, Elsevier, vol. 403(C).

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