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两种有效的非线性共轭梯度算法 被引量：3

TWO EFFICIENT NONLINEAR CONJUGATE GRADIENT METHODS
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摘要 根据CG-DESCENT算法[1]的结构和Powell在综述文献[11]中的建议,给出了两种新的求解无约束优化问题的非线性共轭梯度算法.它们在任意线搜索下都具有充分下降性质,并在标准Wolfe线搜索下对一般函数能够保证全局收敛性.通过对CUTEr函数库中部分著名的函数进行试验,并借助著名的Dolan & More[2]评价方法,展示了新算法的有效性. By the structure of CG-DESCENT method and Powell＇s suggestion in , two effi- cient nonlinear conjugate gradient methods are given. The given methods can be guaranteed the sufficient descent property without out any line search, and be proved the global conver- gence property for the general functions under the standard Wolfe line search. In particular, by the famous evaluation method of Dolan 8z More, the numerical results also show that the proposed methods are more efficient by comparing with the famous CG-DESCENT method using a classical set of problems from CUTEr library.
作者 刘金魁
机构地区 重庆三峡学院数学与统计学院
出处 《计算数学》 CSCD 北大核心 2013年第3期286-296,共11页 Mathematica Numerica Sinica
基金 重庆市教委项目(KJ121112)
关键词 非线性共轭梯度法 标准Wolfe线搜索 充分下降性质 全局收敛性 nonlinear conjugate gradient method standard Wolfe line search sufficientdescent property global convergence property
分类号 O224 [理学—运筹学与控制论]
  • 相关文献

参考文献13

  • 1Hager W W and Zhang H. A new conjugate gradient method with guaranteed descent and an efficient line search[J]. SIAM Journal on Optimization, 2005, 16: 170-192.
  • 2Dolan E D and More J J. Benchmarking optimization software with performance profiles[J]. Mathematical Programming, 2002, 91: 201-213.
  • 3Hestenes M R. Iterative method for sovling linear equations, NANL Report No 53-9, National Bureau of Standards, Washington, D.C. 1951(later published in JOTA, 1973, 1:322-334).
  • 4Stiefel E L. Uber einige Methodern der Relationsrechnung, Zeitschrifit f/ir Angewandte Mathe- matik under Physik 1952, 3.
  • 5Fletcher R, Reeves C. Fenction minimization by conjugate gradients[J]. Computer Journal, 1964, 7: 149-154.
  • 6Hestenes M R, Stiefel E L. Methods of conjugate gradients for solving linear systems[J]. J Res Nat Bur Standards Sect. 1952, 5: 409-436.
  • 7Liu Y and Story C. E fficient generalized conjugate gradient algorithms. Part 1: Theory, J. Optimize. Theory Appl. 1992, 69: 129-137.
  • 8Polak E, Ribire G. Note sur la xonvergence de directions conjugees[J]. Rev Francaise informat Recherche Operatinelle 3e Annee 1969, 16: 35-43.
  • 9Polak B T, The conjugate gradient method in extreme problems[J]. USSR Comput. Math. Math. Phys., 1969, 9: 94-112.
  • 10Dai Y H, Yuan Y X. Nonlinear Conjugate Cradient with a Strong Global Convergence Property[J]. SIAM Journal of Optimization, 2000, 10: 177-182.

同被引文献20

  • 1Hestenes M R,Stiefel E L.Methods of conjugate gradients for solving linear systems[J].Journal of Research of the National Bureau of Standards,1952,49(6):409-436.
  • 2Fletcher R,Reeves C.Function minimization by conjugate gradients[J].Computer Journal,1964,7(2):149-154.
  • 3Liu Y,Story C.Efficient generalized conjugate gradient algorithms,Part 1:Theory[J].Journal of Optimization and Theory Applications,1992,69(1):129-137.
  • 4Polak E,Ribire G.Note sur la xonvergence de directions conjugees[J].Rev Francaise informat Recherche Operatinelle 3e Annee,1969,16:35-43.
  • 5Polak B T.The conjugate gradient method in extreme problems[J].USSR Computational Mathematics and Mathematical Physics,1969,9(4):94-112.
  • 6Dai Y H,Yuan Y X.Nonlinear conjugate gradient with a strong global convergence property[J].*SIAM Journal on Optimization,2000,10(1):177-182.
  • 7Hager W W,Zhang H.A new conjugate gradient method with guaranteed descent and an efficient line search[J].SIAM Journal on Optimization,2005,16(1):170-192.
  • 8Powell M J D.Nonconvex minimization calculations and the conjugate gradient method[M].in Numerical Analysis(Dundee,1983),vol.1066 of Lecture Notes in Mathematics,pp.122-141,Springer,Berlin,Germany,1984.
  • 9Powell M J D.Convergence properties of algorithms for nonlinear optimization[J].SIAM Review,1986,28(4):487-500.
  • 10Gilbert J C,Nocedal J.Global convergence properties of conjugate gradient methods for optimization[J].SIAM Journal on Optimization,1992,2(1):21-42.

引证文献3

二级引证文献10

计算数学
2013年 第3期

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