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Global minimization of non-smooth unconstrained problems with filled function

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Abstract

For smooth or non-smooth unconstrained global optimization problems, an one parameter filled function is derived to identify their global optimizers or approximately global optimizers. The theoretical properties of the proposed function are investigated. Based on the filled function, an algorithm is designed for solving unconstrained global optimization problems. The algorithm consists of two phases: local minimization and filling. The former is intended to minimize the objective function and obtain a local optimizer, the latter aims to find a better initial point for the first phase. Numerical experimentation is also provided. The preliminary computational results confirm that the proposed filled function approach is promising.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Second Polytechnic University, Shanghai, 201209, China

    W. X. Wang

  2. Department of Mathematics, Henan University of Science and Technology, Luoyang, 471003, China

    Y. L. Shang

  3. Department of Mathematics, Shanghai University, Shanghai, 200436, China

    L. S. Zhang

  4. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Y. Zhang

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  1. W. X. Wang
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  2. Y. L. Shang
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  3. L. S. Zhang
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  4. Y. Zhang
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Correspondence to W. X. Wang.

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Wang, W.X., Shang, Y.L., Zhang, L.S. et al. Global minimization of non-smooth unconstrained problems with filled function. Optim Lett 7, 435–446 (2013). https://doi.org/10.1007/s11590-011-0427-7

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  • DOI: https://doi.org/10.1007/s11590-011-0427-7

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