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An Inexact Newton Method Derived from Efficiency Analysis

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Abstract

We consider solving an unconstrained optimization problem by Newton-PCG like methods in which the preconditioned conjugate gradient method is applied to solve the Newton equations. The main question to be investigated is how efficient Newton-PCG like methods can be from theoretical point of view. An algorithmic model with several parameters is established. Furthermore, a lower bound of the efficiency measure of the algorithmic model is derived as a function of the parameters. By maximizing this lower bound function, the parameters are specified and therefore an implementable algorithm is obtained. The efficiency of the implementable algorithm is compared with Newton’s method by theoretical analysis and numerical experiments. The results show that this algorithm is competitive.

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Authors and Affiliations

  1. China Agricultural University, 100083, Beijing, China

    Naiyang Deng & Ping Zhong

  2. Beijing Polytechnic University, 100022, Beijing, China

    Yi Xue

  3. City University of Hong Kong, Hong Kong

    Jianzhong Zhang

Authors
  1. Naiyang Deng
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  2. Yi Xue
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  3. Jianzhong Zhang
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  4. Ping Zhong
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Corresponding author

Correspondence to Naiyang Deng.

Additional information

Mathematics Subject Classification: 90C30, 65K05.

This work was supported by the National Science Foundation of China Grant No. 10371131, and Hong Kong Competitive Earmarked Research Grant CityU 1066/00P from Hong Kong University Grant Council

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Deng, N., Xue, Y., Zhang, J. et al. An Inexact Newton Method Derived from Efficiency Analysis. J Glob Optim 31, 287–315 (2005). https://doi.org/10.1007/s10898-004-5701-0

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  • DOI: https://doi.org/10.1007/s10898-004-5701-0

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