A Nonmonotone Line Search Method for Regression Analysis

In this paper, we propose a nonmonotone line search combining with the search direction (G. L. Yuan and Z. X.Wei, New Line Search Methods for Unconstrained Optimization, Journal of the Korean Statistical Society, 38(2009), pp. 29-39.) for regression problems. The global convergence of the given method will be established under suitable conditions. Numerical results show that the presented algorithm is more competitive than the normal methods.

[1]  Martin Mächler,et al.  Robust regression:a weighted least squares approach , 1997 .

[2]  Defeng Sun,et al.  Global convergece of the bfgs algorithm with nonmonotone linesearch ∗ ∗this work is supported by national natural science foundation$ef: , 1995 .

[3]  Franklin A. Graybill,et al.  Regression Analysis-Concepts and Applications , 1995 .

[4]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[5]  Guanghui Liu,et al.  Global Convergence Analysis of a New Nonmonotone BFGS Algorithm on Convex Objective Functions , 1997, Comput. Optim. Appl..

[6]  William W. Hager,et al.  A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization , 2004, SIAM J. Optim..

[7]  Zhang Xue-song Practical Method of Optimization of Cable Tensions for Cable-stayed Bridges , 2003 .

[8]  R. H. Myers Classical and modern regression with applications , 1986 .

[9]  Ya-Xiang Yuan,et al.  A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property , 1999, SIAM J. Optim..

[10]  DaiYuhong,et al.  A NONMONOTONE CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION , 2002 .

[11]  A. C. Rencher Methods of multivariate analysis , 1995 .

[12]  Johannes Schropp A note on minimization problems and multistep methods , 1997 .

[13]  Wei Zeng-xin,et al.  New Two-Point Stepsize Gradient Methods for Solving Unconstrained Optimization Problems , 2007 .

[14]  L. Grippo,et al.  A nonmonotone line search technique for Newton's method , 1986 .

[15]  L. Grippo,et al.  A truncated Newton method with nonmonotone line search for unconstrained optimization , 1989 .

[16]  Jorge Nocedal,et al.  Global Convergence Properties of Conjugate Gradient Methods for Optimization , 1992, SIAM J. Optim..

[17]  A. Renshaw,et al.  Generalised linear models and excess mortality from peptic ulcers , 1990 .

[18]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[19]  Steven Haberman,et al.  Generalized linear models and actuarial science , 1996 .

[20]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[21]  S. Chatterjee,et al.  Regression Analysis by Example , 1979 .

[22]  Xiwen Lu,et al.  A modified PRP conjugate gradient method , 2009, Ann. Oper. Res..

[23]  John Fox,et al.  Linear Statistical Models and Related Methods; With Applications to Social Research. , 1985 .

[24]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[25]  E. Polak,et al.  Note sur la convergence de méthodes de directions conjuguées , 1969 .

[26]  M. N. Vrahatisa,et al.  A class of gradient unconstrained minimization algorithms with adaptive stepsize , 1999 .

[27]  Liying Liu,et al.  The convergence properties of some new conjugate gradient methods , 2006, Appl. Math. Comput..

[28]  C. Storey,et al.  Efficient generalized conjugate gradient algorithms, part 1: Theory , 1991 .

[29]  Guoyin Li,et al.  New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems , 2006, Appl. Math. Comput..

[30]  N. Draper,et al.  Applied Regression Analysis: Draper/Applied Regression Analysis , 1998 .

[31]  M. N. Vrahatis,et al.  A class of gradient unconstrained minimization algorithms with adaptive stepsize - some corrections , 2000 .

[32]  Zengxin Wei,et al.  The superlinear convergence analysis of a nonmonotone BFGS algorithm on convex objective functions , 2008 .

[33]  Eric R. Ziegel,et al.  Handbook of Nonlinear Regression Models , 1991 .

[34]  D. J. van Wyk Differential optimization techniques , 1984 .

[35]  R. R. Hocking The analysis and selection of variables in linear regression , 1976 .

[36]  Zengxin Wei,et al.  New line search methods for unconstrained optimization , 2009 .

[37]  Robert L. Mason,et al.  Regression Analysis and Its Application: A Data-Oriented Approach. , 1982 .

[38]  Bruce E. Barrett Regression Analysis: Concepts and Applications , 1994 .

[39]  Muni S. Srivastava,et al.  Regression Analysis: Theory, Methods, and Applications , 1991 .

[40]  David A. Ratkowsky,et al.  Handbook of nonlinear regression models , 1990 .

[41]  Gonglin Yuan,et al.  Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems , 2009, Optim. Lett..

[42]  Marcos Raydan,et al.  The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem , 1997, SIAM J. Optim..

[43]  P. Sprent,et al.  Nonlinear Regression Modeling-A Unified Practical Approach. , 1985 .

[44]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[45]  Ronald Christensen,et al.  Analysis of Variance, Design, and Regression: Applied Statistical Methods , 1996 .

[46]  Jorge J. Moré,et al.  Testing Unconstrained Optimization Software , 1981, TOMS.

[47]  Tang Huan-wen A New Line Search Method for Unconstrained Optimization , 2005 .

[48]  Johannes Schropp One-step and multistep procedures for constrained minimization problems , 2000 .

[49]  R. Kass Nonlinear Regression Analysis and its Applications , 1990 .

[50]  L. Grippo,et al.  A class of nonmonotone stabilization methods in unconstrained optimization , 1991 .