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求解单调非线性方程组的凸组合算法的收敛性 被引量：3

The global convergence of the algorithm of convexly combinations for solving monotone nonlinear equations
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摘要 将求解单调非线性方程组的MPRP算法和CGD算法的下降方向进行凸组合,构造出新的下降方向,提出新的算法,并证明新算法是全局收敛的. By convexly combining the the descent directions of the MPRP algorithm and the CGD algorithm for solving monotone nonlinear equations, the new descent direction was constructed, the new algorithm and its global convergence were put forward.
作者 王胜 关洪波
机构地区 湖南工学院数理部
出处 《湖南文理学院学报（自然科学版）》 CAS 2013年第2期16-19,共4页 Journal of Hunan University of Arts and Science(Science and Technology)
基金 湖南省教育厅资助项目(12C0664) 湖南工学院院级项目(HY11006 HY12007)
关键词 凸组合 单调非线性方程组 全局收敛性 convexly combination monotone nonlinear equations globally convergent
分类号 O241.7 [理学—计算数学]
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参考文献6

  • 1Zhou W J, Li D H. Limited memory BFGS method for nonlinear monotone equations!J]. Journal of Computational andApplied Mathematics, 2007,25: 89~96. 被引量：1
  • 2Yan Q R, Peng X Z, Li D H. A globally convergent derivative-free method for solving large-scale nonlinear monotoneequations[J]. Journal of Computational and Applied Mathematics, 2010,234(3): 649~957. 被引量：1
  • 3Dai Y H, Yuan Y. A nonlinear conjugate gradient method with a strong global convergebce property [J], SIAM Journal onOptimization, 1999,10(1): 177—182. 被引量：1
  • 4Zhou W J, Li D H. Limited memory BFGS method for nonlinear monotone equations[J]. Journal of Computational andApplied Mathematics, 2007,25: 89—96. 被引量：1
  • 5Xiao Y H, Zhu H. A conjugate gradient method to solve convex constrained monotone equations with applications incompressive sensing[EB/OL]. Journal of Mathematical Analysis and Applications, http://dx.d0i.0rg/l 0.1016/j .jmaa.2013-04-017. 被引量：1
  • 6Zhang L, Zhou W J, Li D H. A descent modified Polak-Ribidre-Polyak conjugate gredient method and its global.convergence[J]. IMA Journal of Numerical Analysis, 2006,26(4): 629—940. 被引量：1

同被引文献17

  • 1Zhou W J, Li D H. A globally convergent BFGS method for nonlinear monotone equations without any merit functions [ J ]. Mathematics of Computation, 2008,77 ( 264 ) : 2231-2240. 被引量：1
  • 2Yan Q R,Peng X Z,Li D H. A globally convergent derivative-free method for solving large- scale nonlinear monotone equations[J]. Journal of Corn-putational and Applied Mathematics, 2010,234 (3) : 649-957. 被引量：1
  • 3Zhou W J,Li D H. Limited memory BFGS method for nonlinear monotone equations [ J ]. Journal of Computational and Applied Mathematics,2007,25: 89-96. 被引量：1
  • 4Zhang L, Zhou W J, Li D H. A descent modified Polak- Ribi:re - Polyak conjugate gredient method and its global convergence [ ] ]. IMA Journal of Numerical Analysis, 2006,26 (4) :629-940. 被引量：1
  • 5Xiao Y H, Zhu H. A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing. Journal of Mathematical Analysis and Applications [ EB/ OL]. http://dx, doi. org/10. 1016/j. jmaa, 2013- 04-17. 被引量：1
  • 6Zhou W J,Li D H. Limited memory BFGS method for nonlinear monotone equations[J].Journal of Computational and Applied Mathematics,2007.89-96. 被引量：1
  • 7Zhou W J,Li D H. A globally convergent BFGS method for nonlinear monotone equations without any merit functions[J].Mathematics of Computation,2008,(264):2231-2240.doi:10.1090/S0025-5718-08-02121-2. 被引量：1
  • 8Yan Q R,Peng X Z,Li D H. A globally convergent derivative-free method for solving large-scale nonlinear monotone equations[J].Journal of Computational and Applied Mathematics,2010,(03):649-957. 被引量：1
  • 9Zhang L,Zhou W J,Li D H. A descent modified Polak-Ribière-Polyak conjugate gredient method and its global convergence[J].IMA Journal of Numerical Analysis,2006,(04):629-940. 被引量：1
  • 10Xiao Y H,Zhu H. A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing[J].Journal of Mathematical Analysis and Applications,2013,(01). 被引量：1

引证文献3

湖南文理学院学报（自然科学版）
2013年 第2期

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