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三项共轭梯度法收敛性分析 被引量:8

CONVERGENCE OF THREE-TERM CONJUGATE GRADIENT METHODS
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摘要 This paper studies the three-term conjugate gradient method for unconstrained optimization. The method includes the classical (two-term) conjugate gradient method and the famous Beale-Powell restart algorithm as its special forms. Some mild conditions are given in this paper, which ensure the global convergence of general three-term conjugate gradient methods. This paper studies the three-term conjugate gradient method for unconstrained optimization. The method includes the classical (two-term) conjugate gradient method and the famous Beale-Powell restart algorithm as its special forms. Some mild conditions are given in this paper, which ensure the global convergence of general three-term conjugate gradient methods.
出处 《计算数学》 CSCD 北大核心 1999年第3期355-362,共8页 Mathematica Numerica Sinica
基金 国家自然科学基金!19525101 19731010 19801033
关键词 无约束优化 共轭梯度法 线搜索 全局收敛 收敛性 Unconstrained optimization, Conjugate gradient, Line search, Global convergence
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参考文献6

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同被引文献18

  • 1郭文英,徐大川,申贵成.Hestenes-Stiefel共轭梯度法的全局收敛性[J].科学通报,1995,40(23):2113-2117. 被引量:6
  • 2BEALE E M L. A derivative of conjugate gradients[ C]// LOOTSMA F A. Numerical methods for nonlinear optimization. London: Academic Press, 1972 : 3943.
  • 3DENG N Y, LI Z F. Global convergence of three terms conjugate gradient methods[J]. Optimization Method and Software, 1995 (4) :273-282.
  • 4SUN Qing-ying. Global convergence results for a new three terms memory gradient method with Curry-Altmans step size rules [ J ]. Soochow Journal of Mathmatics, 2004,30( 1 ) :55-66.
  • 5BERTSEKAS Dimitri P, TSITSIKLIS John N. Gradient convergence in gradient methods with errors [ J]. SIAM J Optim, 2000 ( 3 ) : 627-642.
  • 6TOUATI-AHMED D, STOREY C. Efficient hybrid conjugate gradient techniques [ J ]. Journal of Optimization Theory and Applications, 1990,64 ( 2 ) : 379 -397.
  • 7DAI Y H, LIAO L Z. New conjugate conditions and related nonlinear conjugate gradient methods [ J ]. Applied Mathematics and Optimization, 2001,43 ( 1 ) :87-101.
  • 8M. J. D. Powell.Restart procedures for the conjugate gradient method[J].Mathematical Programming.1977(1)
  • 9Gilbert J C,Nocedal J.Global convergence properties of conjugate gradient methods for optimization[].SIAM Journal on Optimization.1992
  • 10Beale,E.M.L.A derivative of conjugate gradients[].Numerical methods fononlinear optimization.1972

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