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一种修正的WYL共轭梯度法及其全局收敛性 被引量：1

Global Convergence of A Modified WYL Conjugate Gradient Method
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摘要 文章提出了一种用于求解无约束优化问题的修正的WYL共轭梯度法,该算法在不依赖任何线性搜索的情况能够始终产生充分下降方向.在适当的条件下,采取了Armijo线性搜索的该算法具有全局收敛性,最后,我们给出相应的数值结果说明该算法是有效的. In this paper,we proposed a modified WYL conjugate gradient method for solving un-constrained optimization problem.The method can always generate sufficient descent method independent of any line search used.Under suitable condition,the global convergence with Armijo line search is established.At last,we present numerical results to show thee efficiency of the proposed method.
作者 李灿 黄双双
机构地区 红河学院数学学院 嘉兴学院数理与信息工程学院
出处 《红河学院学报》 2011年第4期23-26,共4页 Journal of Honghe University
关键词 无约束优化问题 共轭梯度法 Armijo线性搜索 充分下降性 全局收敛性 unconstrained optimization problem conjugate gradient method Armijo line search sufficient descent property global convergence
分类号 O29 [理学—应用数学]
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参考文献9

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  • 2Polak,B.T..The conjugate gradient method in extreme problems [J].USSR Comp. Math.Math.Phys., 1969,9:94-112.
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同被引文献16

  • 1POLAK E, RIBIERE G. Note sur la convergence de directions conjugees [ J ]. Rev Francaise Informat Recherche Oper- atinelle, 1969, 16: 35-43.
  • 2DAI Y, YUAN Y. A nonlinear conjugate gradient with a strong global convergence properties [ J ]. SIAM Journal on Opti- mization, 2000, 10: 177-182.
  • 3HESTENES M R, STIEFEL E. Methods of conjugate gradients for solving linear systems [ J ]. Journal of Research National Bureau of Standards : Section B, 1952, 49 : 409-436.
  • 4FLETCHER R, REEVES C. Function minimization by conjugate gradients [J]. Computer Journal, 1964, 7: 149-154.
  • 5LIU Y, STOREY C. Effcient generalized conjugate gradient algorithms [ J]. Journal of Optimization Theory and Applica- tions, 1991, 69: 129-137.
  • 6POLYAK B T. The conjugate gradient method in extreme problems [ J ]. USSR Comput Math Math Phys, 1969, 9 : 94-112.
  • 7YU G H, ZHAO Y L, WEI Z X. A descent nonlinear conjugate gradient method for large-scale unconstrained optimization [J]. Applied Mathematics and Computation, 2007, 187: 636-643.
  • 8YUAN G L, LU X W, WEI Z X. A conjugate gradient method with descent direction for unconstrained optimization [ J~. Journal of Computational and Applied Mathematics, 2009, 233: 519-530.
  • 9YUAN G L, ZHANG M J. A three-terms Polak-Ribi~re-Polyak conjugate gradient algorithm for large-scale nonlinear equa- tions [J]. Journal of Computational and Applied Mathematics, 2015, 286: 186-195.
  • 10YUAN G L, WEI Z X, ZHAO Q M. A modified Polak-Ribi~re-Polyak conjugate gradient algorithm for large-scale optimiza- tion problems [J]. IIE Transactions, 2014, 46: 397-413.

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红河学院学报
2011年 第4期

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