A sufficient descent conjugate gradient method and its global convergence

In this paper, a DL-type conjugate gradient method is presented. The given method is a modification of the Dai–Liao conjugate gradient method. It can also be considered as a modified LS conjugate gradient method. For general objective functions, the proposed method possesses the sufficient descent condition under the Wolfe line search and is globally convergent. Numerical comparisons show that the proposed algorithm slightly outperforms the PRP+ and CG-descent gradient algorithms as well as the Barzilai–Borwein gradient algorithm.

[1]  Zengxin Wei,et al.  A Conjugate Gradient Method with Global Convergence for Large-Scale Unconstrained Optimization Problems , 2013, J. Appl. Math..

[2]  Zengxin Wei,et al.  A note about WYL's conjugate gradient method and its applications , 2007, Appl. Math. Comput..

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

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

[5]  Ya-Xiang Yuan,et al.  Convergence Properties of Nonlinear Conjugate Gradient Methods , 1999, SIAM J. Optim..

[6]  Duan Li,et al.  On Restart Procedures for the Conjugate Gradient Method , 2004, Numerical Algorithms.

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

[8]  Ya-Xiang Yuan,et al.  Optimization Theory and Methods: Nonlinear Programming , 2010 .

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

[10]  Siam Rfview,et al.  CONVERGENCE CONDITIONS FOR ASCENT METHODS , 2016 .

[11]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[12]  Reza Ghanbari,et al.  A descent family of Dai–Liao conjugate gradient methods , 2014, Optim. Methods Softw..

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

[14]  Shengwei Yao,et al.  A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods , 2014 .

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

[16]  Reza Ghanbari,et al.  The Dai-Liao nonlinear conjugate gradient method with optimal parameter choices , 2014, Eur. J. Oper. Res..

[17]  Yu-Hong Dai,et al.  A Nonlinear Conjugate Gradient Algorithm with an Optimal Property and an Improved Wolfe Line Search , 2013, SIAM J. Optim..

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

[19]  M. Al-Baali.  Descent Property and Global Convergence of the Fletcher—Reeves Method with Inexact Line Search , 1985 .

[20]  Nicholas I. M. Gould,et al.  CUTE: constrained and unconstrained testing environment , 1995, TOMS.

[21]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

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

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

[24]  P. Wolfe.  Convergence Conditions for Ascent Methods. II , 1969 .

[25]  Neculai Andrei,et al.  An Unconstrained Optimization Test Functions Collection , 2008 .