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Flow Search Approach and New Bounds for the m-Step Linear Conjugate Gradient Algorithm

Author

Listed:
  • H. X. Huang

    (Tsinghua University)

  • Z. A. Liang

    (Shanghai University of Finance and Economics)

  • P. M. Pardalos

    (University of Florida)

Abstract

A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to some serial search stages, the stepsize parameters in different search stages may interact mutually, and their optimal values are determined by evaluating the total effect of the interaction. The main idea of the flow search approach is illustrated via the minimization of a convex quadratic function. Based on the flow search approach, some properties of the m-step linear conjugate gradient algorithm are analyzed and new bounds on its convergence rate are also presented. Theoretical and numerical results indicate that the new bounds are better than the well-known ones.

Suggested Citation

  • H. X. Huang & Z. A. Liang & P. M. Pardalos, 2004. "Flow Search Approach and New Bounds for the m-Step Linear Conjugate Gradient Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 53-71, January.
    • Handle: RePEc:spr:joptap:v:120:y:2004:i:1:d:10.1023_b:jota.0000012732.62633.59
    DOI: 10.1023/B:JOTA.0000012732.62633.59
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    Cited by:

    1. Christopher J. Gerry & Igor Sheiman, 2016. "The Health Workforce of the Russian Federation in the Context Of the International Trends," HSE Working papers WP BRP 01/PSP/2016, National Research University Higher School of Economics.

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