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A modified trust region method with Beale’s PCG technique for optimization

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Abstract

It is well-known that the conjugate gradient method is widely used for solving large scale optimization problems. In this paper a modified trust-region method with Beale’s Preconditioned Conjugate Gradient (BPCG) technique is developed for solving unconstrained optimization problems. The modified version adopts an adaptive rule and retains some useful information when an unsuccessful iteration occurs, and therefore improves the efficiency of the method. The behavior and the convergence properties are discussed. Some numerical experiments are reported.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097, China

    Wenyu Sun & Liusheng Hou

  2. Department of Mathematics, Nanjing Xiaozhuang College, Nanjing, China

    Liusheng Hou

  3. Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong

    Chuangying Dang

Authors
  1. Wenyu Sun
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  2. Liusheng Hou
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  3. Chuangying Dang
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Corresponding author

Correspondence to Wenyu Sun.

Additional information

This work was partially supported by Grant of the National Natural Science Foundation of China, Grant: 20040319003 of the Doctoral Site of the Education Ministry of China, and SRG: 7001428 of City University of Hong Kong.

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Sun, W., Hou, L. & Dang, C. A modified trust region method with Beale’s PCG technique for optimization. Comput Optim Appl 40, 59–72 (2008). https://doi.org/10.1007/s10589-007-9078-0

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  • DOI: https://doi.org/10.1007/s10589-007-9078-0

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