THE CONVERGENCE OF BROYDEN ALGORITHMS FOR LC GRADIENT FUNCTION 被引量：1

THE CONVERGENCE OF BROYDEN ALGORITHMS FOR LC GRADIENT FUNCTION

导出

摘要 In this paper, we discuss the convergence of Broyden algorithms for the functions which are non-twice differentiable, but have LC gradient. We prove that the rate of convergence of the algorithms is linear for uniformly convex functions. We also demonstrate that under some mild conditions the algorithms are superlinsarly convergent. In this paper, we discuss the convergence of Broyden algorithms for the functions which are non-twice differentiable, but have LC gradient. We prove that the rate of convergence of the algorithms is linear for uniformly convex functions. We also demonstrate that under some mild conditions the algorithms are superlinsarly convergent.

作者濮定国

出处《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2000年第3期313-319,共7页 应用数学学报（英文版）

关键词 Variable metric algorithms CONVEX CONVERGENCE convergence rate Variable metric algorithms, convex, convergence, convergence rate

分类号 O241 [理学—计算数学]

引文网络
相关文献

参考文献13

1濮定国,田蔚文.一类带非精确线搜索的修改的Broyden算法[J].高校应用数学学报（A辑）,1995,10(3):313-322. 被引量：4
2PU, DG,TIAN, WW.A CLASS OF MODIFIED BROYDEN ALGORITHMS[J].Journal of Computational Mathematics,1994,12(4):366-379. 被引量：6
3Dingguo Pu,Wenci Yu.On the convergence property of the DFP algorithm[J].Annals of Operations Research.1990(1)
4L. C. W. Dixon.Variable metric algorithms: Necessary and sufficient conditions for identical behavior of nonquadratic functions[J].Journal of Optimization Theory and Applications.1972(1)
5D. Pu.Modified DFP Algorithm[].Acta Mithematicae Applicatae Sinica.1989
6L.C.W. Dixon.Variable Metric Algorithms: Necessary and Sufficient Conditions for Identical Behaviorof Nonquadratical Functions[].Journal of Optimization Theory and Applications.1972
7M.J.D. Powell.On the Convergence of the Variable Metric Algorithm[].Inst Math Appl.1971
8M.J.D. Powell.Some global convergence properties of a variable metric algorithm for minimization without exact line searches[]..1976
9F.H. Clarke.Optimization and Nonsmooth Analysis[]..1990
10J.D. Pearson.Variable Metric Method of Minimization[].Computer Journal.1969

二级参考文献11

1濮定国.带线性约束的变尺度算法[J].运筹学杂志,1989,8(1):53-56. 被引量：2
2濮定国，J C M，1994年，12卷，4期，366页
3田蔚文，应用数学与计算数学学报，1993年，7卷，1期，50页
4濮定国，Asia-Pacific J Operational Research，1992年，9卷，2期，207页
5濮定国，上海铁道学院学报，1991年，12卷，3期，72页
6濮定国，上海铁道学院学报，1990年，11卷，4期，79页
7濮定国，应用数学学报，1989年，13卷，1期，118页
8濮定国，上海铁道学院学报，1987年，8卷，3期，9页
9濮定国，An of Oper Res，24卷，175页
10濮定国.一类带非精确线性搜索的 DFP 算法[J].运筹学杂志,1990,9(2):49-50. 被引量：2

共引文献6

1濮定国,王华,田蔚文.带非精确线搜索的调整搜索方向DFP算法(英文)[J].运筹学学报,2004,8(3):1-9. 被引量：5
2李霞,桂胜华.改进的不带线搜索的两参数簇共轭梯度方法[J].上海第二工业大学学报,2004,21(2):9-15.
3PUDingguo,TIANWeiwen.A CLASS OF REVISED BROYDEN ALGORITHMS[J].Journal of Systems Science & Complexity,2003,16(2):213-221. 被引量：1
4濮定国.带下降方向搜索的总极值方法[J].应用数学与计算数学学报,1996,10(2):51-56.
5TIAN Weiwen (Shanghai University, Shanghai 200436, China) PU Dingguo (Tongji University, Shanghai 200333, China).CONVERGENCE PROPERTIES OF DFP METHOD WITH MODIFIED QUASI-NEWTON EQUATIONS[J].Journal of Systems Science & Complexity,2001,14(3):293-305.
6Ding-guoPu Sheng-huaGui Wei-wenTian.A CLASS OF REVISED BROYDEN ALGORITHMS WITHOUT EXACT LINE SEARCH[J].Journal of Computational Mathematics,2004,22(1):11-20. 被引量：8

同被引文献5

1M. J. D. Powell.Some global convergence properties of a variable metric algorithm for minimization without exact line searches[].SIAM Journal on Nonlinear Programming.1976
2D. Pu,W. Yu.On the Convergence Property of the DFP Algorithm[].Journal of Annual of OperationsResearch.1990
3M.J.D. Powell.On the Convergence of the Vaiable Metric Algorithm[].Journal of the InstituteMathematics and its Applications.1971
4D. Pu.A Class of DFP Algorithm without Exact Linear Search[].Asia Pacific Journal of Operational Research.1992
5R.H. Byrd,J. Nocedal,Y. Yuan.Global Convergence of a Class of Quasi-Newton Methods on ConvexProblems[].SIAM Journal on Numerical Analysis.1987

引证文献1

1濮定国.SUPERLINEAR CONVERGENCE OF THE DFP ALGORITHM WITHOUT EXACT LINE SEARCH[J].Acta Mathematicae Applicatae Sinica,2001,17(3):430-432.

1PU Dingguo(Institute of Applied Mathematics, Shanghai Tiedao University, Shanghai 200333, China).THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION[J].Systems Science and Mathematical Sciences,1997,10(4):289-298.
2PU, DG,TIAN, WW.A CLASS OF MODIFIED BROYDEN ALGORITHMS[J].Journal of Computational Mathematics,1994,12(4):366-379. 被引量：6
3PUDingguo,TIANWeiwen.A CLASS OF REVISED BROYDEN ALGORITHMS[J].Journal of Systems Science & Complexity,2003,16(2):213-221. 被引量：1
4Ding-guoPu Sheng-huaGui Wei-wenTian.A CLASS OF REVISED BROYDEN ALGORITHMS WITHOUT EXACT LINE SEARCH[J].Journal of Computational Mathematics,2004,22(1):11-20. 被引量：8
5Cong-ying HAN,Fang-ying ZHENG,Tian-de GUO,Guo-ping HE.Parallel Algorithms for Large-scale Linearly Constrained Minimization Problem[J].Acta Mathematicae Applicatae Sinica,2014,30(3):707-720.
6XU Chen,PENG ZhiMing,JING WenFeng.Sparse kernel logistic regression based on L_(1/2) regularization[J].Science China(Information Sciences),2013,56(4):71-86. 被引量：5

Acta Mathematicae Applicatae Sinica

2000年第3期

浏览历史

内容加载中请稍等...