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界约束非线性方程组的仿射尺度内点信赖域法 被引量：1

An Affine-scaling Interior-point Trust Region Method for Nonlinear Equations with Simple Bounds
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摘要 提出用一种非单调仿射尺度内点信赖域方法求解简单界约束非线性方程组,该算法使用非单调结构,放宽了接受尝试步的条件,在通常假设条件下,证明了算法的全局收敛性。 This paper presents an affine scaling interior-point trust region method for solving nonlinear equations with simple bounds. By compiling the program with Matlab, the numerical tests show that this new method is very effective.
作者 夏红卫
机构地区 常州工学院理学院
出处 《常州工学院学报》 2006年第5期43-48,共6页 Journal of Changzhou Institute of Technology
关键词 非线性方程组 界约束 内点信赖域方法 nonlinear equations simple bounds interior-point trust region method
分类号 O221.2 [理学—运筹学与控制论]
  • 相关文献

参考文献8

  • 1[1]Bellavia S,Macconi M,Morini B.An affine scaling trust-region approach to bound-constrained nonlinear systems[J].Appl.Nummer.Math.,2003,44(3):257-280.
  • 2[2]Bellavia S,Macconi M,Morini B.A scaled trust-region solver for constrained nonlinear equations[J].Comp.Optim.Appl.,2004,28(1),31-50.
  • 3[3]Fransico J B,Krejic N,Martinez J M.An interior-point method for solving box-constrained underdetermined nonliear systems[J].J.Comp.Appl.Math.,2005,177(1):67-88.
  • 4[4]Dan N,Yamashita Y,Fukushima M.Convergence properties of inexact Levenberg-Marquardt method under local error bound conditions[J].Optim.Methods Software,2002,17(4):605-626.
  • 5[5]Fan J,Yuan X.On the quadratic convergence of the levenberg-marquardt method without nonsingularity assumption[J].Computing,2005,74(1):23-39.
  • 6郭楠.凸约束非线性方程组的非单调投影L-M方法[J].苏州大学学报（自然科学版）,2006,22(1):10-14. 被引量：6
  • 7[7]Heinkenschloss M,Ulbrich M,Ulbrich S.Superlinear and quadratic convergence of affine scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption[J].Math.Prog.,1999,86(3):615-635.
  • 8刘静,王平,陈中文.简单界约束优化的仿射尺度内点信赖域算法的收敛性[J].应用数学学报,2005,28(1):114-123. 被引量：3

二级参考文献9

  • 1Coleman T F, Li Y. An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds.SIAM J. Optim., 1996, 6:418-445.
  • 2Conn A R, Gould N I M, Toint Ph L. Testing a Class of Methods for Solving Minimization Problems with Simple Bounds on the Variables. Math Comp., 1988, 50:399-430.
  • 3Yin H, Han J. A New Interior Point Trust Region Algorithm for Nonlinear Minimization Problems with Simple Bound Constraints. Presentation at the International Conference on Nonlinear Programming and Variational Inequalities, Hong Kong, 1998.
  • 4Lescrenier M. Convergence of Trust Region Algorithms for Optimization with Bounds when Strict Complementarity does not Hold. SIAM J. Numer. Anal., 1991, 28:476-495.
  • 5Lin C. Moré J J. Newton's Method for Large Bound-constrained Optimization Problems. SIAM J.Optim., 1999, 9:1100-1127.
  • 6Heinkenschloss M, Ulbrich M, Ulbrich S. Superlinear and Quadratic Convergence of Affine-scaling Interior-point Newton Methods for Problems with Simple Bounds without Strict Complementarity Assumption. Math. Prog., (Series A), 1999, 86:615-635.
  • 7FRANSINCO J B, KREJIC N, MARTINEZ J M. An interio-point method for solving boxconstrained underdetermined nonliear systems[J]. Joural of Computational and Applied Mathematics, 2005,177: 65 - 88.
  • 8CALAMAI P H, MORE J J. Projected gradient methods for linearly constrained problems[J]. Math Prog, 1987,39:93- 116.
  • 9CHRISTIAN K, NOBUO Y, MASAO F. Levenberg-Marquardt Methods for Constrained Nonlinear Equations with Strong Local Convergence Properties[R]. Technical Report, 2002.

共引文献5

同被引文献5

  • 1郭楠.凸约束非线性方程组的非单调投影L-M方法[J].苏州大学学报（自然科学版）,2006,22(1):10-14. 被引量：6
  • 2[1]Fransico J B,Krejic N,Martinez J M.An interior-point method for solving box -constrained underdetermined nonliear systems[J],J.Comp.Appl.Math.,2005,177(1):67 -88.
  • 3[2]Bellavia S,Macconi M,Morini B.An affine scaling trust-region approach to bound-constrained nonlinear systems[J],Appl.Nummer.Math.,2003,44(3):257 -280.
  • 4[3]Fan J,Yuan X.On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption[J],Computing,2005,74(1):23 -39.
  • 5[6]Bongartz I,Conn A R,Gould N I M,et al.CUTE:Constrained and unconstrained testing environments[M].Software ACM Trans.Math.1995 (21):123-160.

引证文献1

常州工学院学报
2006年 第5期

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