求解非线性方程组的一种修正WPRP共轭梯度算法
|
摘要
对于求解非线性方程组问题,基于现有的PRP算法,提出了一种改进的PRP算法,并在适定条件下证明了该算法具有全局收敛性。数值实验表明该方法与通常方法相比更具竞争性,对于求解非线性方程组问题是有效的。
For solving the problems of nonlinear equations,an improved PRP algorithm is proposed based on the existing PRP algorithms. The proposed algorithm is proved to be globally convergent under suitable conditions. Numerical experiments show that this method is more competitive than the usual methods and is effective for solving nonlinear equations.
For solving the problems of nonlinear equations,an improved PRP algorithm is proposed based on the existing PRP algorithms. The proposed algorithm is proved to be globally convergent under suitable conditions. Numerical experiments show that this method is more competitive than the usual methods and is effective for solving nonlinear equations.
引文
[1]FLETCHER R.Function minimization by conjugate gradients[J].Computer Journal,1964,7(2):149-154.
[2]POLYAK B T.The conjugate gradient method in extremal problems[J].Ussr Computational Mathematics&Mathematical Physics,1969,9(4):94-112.
[3]段侠彬,袁功林,王晓亮,等.一种含参数的修正HS共轭梯度法及其收敛性[J].广西大学学报(自然科学版),2015,40(3):750-757.
[4]POLAK E,RIBIRE G.Note sur la convergence de méthodes de directions conjuguées.[J].Rev.franaise Informat.recherche Opérationnelle,1968,16(16):35-43.
[5]DAI Y,YUAN Y.A Nonlinear conjugate gradient method with a strong global convergence property[J].Siam Journal on Optimization,1999,10(1):177-182.
[6]时贞军.改进HS共轭梯度算法及其全局收敛性[J].计算数学,2001,23(4):393-406.
[7]WEI Z,YAO S,LIU L.The convergence properties of some new conjugate gradient methods[J].Applied Mathematics&Computation,2006,183(2):1341-1350.
[8]徐泽水.一类新的共轭梯度法[J].数学杂志,2002,22(1):27-30.
[9]YUAN G,LU X.A new backtracking inexact BFGS method for symmetric nonlinear equations[J].Computers&Mathematics with Applications,2008,55(1):116-129.
[10]LI Q,LI D.A class of derivative-free methods for large-scale nonlinear monotone equations[J].Ima Journal of Numerical Analysis,2011,31(4):1625-1635.
[11]YUAN G.Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems[J].Optimization Letters,2009,3(1):11-21.
[12]YUAN G,ZHANG M.A three-terms Polak-Ribière-Polyak conjugate gradient algorithm for large-scale nonlinear equations[J].Journal of Computational&Applied Mathematics,2015,286:186-195.
[13]SOLODOV M V.SVAITER B F.A Globally Convergent Inexact Newton Method for Systems of Monotone Equations[M]//Reformulation:Nonsmooth,Piecewise Smooth,Semismooth and Smoothing Methods.Springer US,1998:1411-1414.
[14]RAYDAN M.The barzilai and borwein gradient method for the large scale unconstrained minimization problem[J].Siam Journal on Optimization,1997,7(1):26-33.
[15]BING Y,LIN G.An efficient implementation of merrill's method for sparse or partially separable systems of nonlinear equations[J].Siam Journal on Optimization,1991,1(2):206-221.
[16]ROBERTS S M,SHIPMAN J S.On the closed form solution of Troesch's problem[J].Journal of Computational Physics,1976,21(3):291-304.
[17]YUAN G,WEI Z,LU X.A BFGS trust-region method for nonlinear equations[J].Computing,2011,92(4):317-333.
[2]POLYAK B T.The conjugate gradient method in extremal problems[J].Ussr Computational Mathematics&Mathematical Physics,1969,9(4):94-112.
[3]段侠彬,袁功林,王晓亮,等.一种含参数的修正HS共轭梯度法及其收敛性[J].广西大学学报(自然科学版),2015,40(3):750-757.
[4]POLAK E,RIBIRE G.Note sur la convergence de méthodes de directions conjuguées.[J].Rev.franaise Informat.recherche Opérationnelle,1968,16(16):35-43.
[5]DAI Y,YUAN Y.A Nonlinear conjugate gradient method with a strong global convergence property[J].Siam Journal on Optimization,1999,10(1):177-182.
[6]时贞军.改进HS共轭梯度算法及其全局收敛性[J].计算数学,2001,23(4):393-406.
[7]WEI Z,YAO S,LIU L.The convergence properties of some new conjugate gradient methods[J].Applied Mathematics&Computation,2006,183(2):1341-1350.
[8]徐泽水.一类新的共轭梯度法[J].数学杂志,2002,22(1):27-30.
[9]YUAN G,LU X.A new backtracking inexact BFGS method for symmetric nonlinear equations[J].Computers&Mathematics with Applications,2008,55(1):116-129.
[10]LI Q,LI D.A class of derivative-free methods for large-scale nonlinear monotone equations[J].Ima Journal of Numerical Analysis,2011,31(4):1625-1635.
[11]YUAN G.Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems[J].Optimization Letters,2009,3(1):11-21.
[12]YUAN G,ZHANG M.A three-terms Polak-Ribière-Polyak conjugate gradient algorithm for large-scale nonlinear equations[J].Journal of Computational&Applied Mathematics,2015,286:186-195.
[13]SOLODOV M V.SVAITER B F.A Globally Convergent Inexact Newton Method for Systems of Monotone Equations[M]//Reformulation:Nonsmooth,Piecewise Smooth,Semismooth and Smoothing Methods.Springer US,1998:1411-1414.
[14]RAYDAN M.The barzilai and borwein gradient method for the large scale unconstrained minimization problem[J].Siam Journal on Optimization,1997,7(1):26-33.
[15]BING Y,LIN G.An efficient implementation of merrill's method for sparse or partially separable systems of nonlinear equations[J].Siam Journal on Optimization,1991,1(2):206-221.
[16]ROBERTS S M,SHIPMAN J S.On the closed form solution of Troesch's problem[J].Journal of Computational Physics,1976,21(3):291-304.
[17]YUAN G,WEI Z,LU X.A BFGS trust-region method for nonlinear equations[J].Computing,2011,92(4):317-333.