Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems

It is well known that the sufficient descent condition is very important to the global convergence of the nonlinear conjugate gradient method. In this paper, some modified conjugate gradient methods which possess this property are presented. The global convergence of these proposed methods with the weak Wolfe–Powell (WWP) line search rule is established for nonconvex function under suitable conditions. Numerical results are reported.

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

[2]  M. Powell.  Nonconvex minimization calculations and the conjugate gradient method , 1984 .

[3]  L. Liao,et al.  New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods , 2001 .

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

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

[6]  Boris Polyak.  The conjugate gradient method in extremal problems , 1969 .

[7]  William W. Hager,et al.  Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent , 2006, TOMS.

[8]  William W. Hager,et al.  A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search , 2005, SIAM J. Optim..

[9]  B. V. Shah,et al.  Integer and Nonlinear Programming , 1971 .

[10]  Wufan Chen,et al.  Spectral conjugate gradient methods with sufficient descent property for large-scale unconstrained optimization , 2008, Optim. Methods Softw..

[11]  W. Hager,et al.  A SURVEY OF NONLINEAR CONJUGATE GRADIENT METHODS , 2005 .

[12]  Guoyin Li,et al.  New conjugacy condition and related new conjugate gradient methods for unconstrained optimization , 2007 .

[13]  Weijun Zhou,et al.  A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence , 2006 .

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

[15]  M. Powell.  Convergence properties of algorithms for nonlinear optimization , 1986 .

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

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

[18]  Jorge J. Moré,et al.  Benchmarking optimization software with performance profiles , 2001, Math. Program..

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