Convergence of memory gradient methods

References

• Barzilai , J. and Borwein , J. M. 1988 . Two point step size gradient methods . IMA J. Numer. Anal. , 8 : 141 – 148 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N. I.M. and Toint , P. L. 1999 . “ Trust-Region Methods ” . CGT productions .
   Google Scholar
• La Cruz , W. and Raydan , M. 2003 . Nonmonotone spectral methods for large-scale nonlinear systems . Optim. Methods Softw. , 18 : 583 – 599 .
   Web of Science ®Google Scholar
• Dai , Y. H. and Yuan , Y. 2005 . Analysis of monotone gradient methods . J. Ind. Manag. Optim. , 1 : 181 – 192 .
   Web of Science ®Google Scholar
• Dai , Y. H. and Liao , L. Z. 2002 . R-linear convergence of the Barzilai and Borwein gradient method . IMA J. Numer. Anal. , 22 : 1 – 10 .
   Web of Science ®Google Scholar
• Dai , Y. H. and Yuan , Y. 2000 . “ Nonlinear Conjugate Gradient Method ” . Shanghai Science and Technology Publisher .
   Google Scholar
• Dai , Y. H. and Xu , D. C. 2003 . A new family of trust region algorithms for unconstrained optimization . J. Comput. Math. , 21 : 221 – 228 .
   Google Scholar
• Fletcher , R. 1987 . “ Practical Methods of Optimization, Vol. I: Unconstrained Optimization ” . John Wiley & Sons, New York .
   Google Scholar
• Gilbert , J. C. and Nocedal , J. 1992 . Global convergence properties of conjugate gradient methods for optimization . SIAM J. Optim. , 2 : 21 – 42 .
   Web of Science ®Google Scholar
• Han , Q. M. , Sun , W. Y. , Han , J. Y. and Sampaio , R. J.B. 2005 . An adaptive conic trust-region method for unconstrained optimization . Optim. Methods Softw. , 20 : 665 – 677 .
   Web of Science ®Google Scholar
• Liu , D. C. and Nocedal , J. 1989 . On the limited memory BFGS method for large scale optimization . Math. Prog. , 45 : 503 – 528 .
   Web of Science ®Google Scholar
• Moré , J. J. , Garbow , B. S. and Hillstrom , K. E. 1981 . Testing unconstrained optimization software . ACM Trans. Math. Softw. , 7 : 17 – 41 .
   Web of Science ®Google Scholar
• Miele , A. and Cantrell , J. W. 1969 . Study on a memory gradient method for the minmization of functions . J. Optim. Theory Appl. , 3 ( 6 ) : 459 – 470 .
   Google Scholar
• Nocedal , J. and Wright , S. J. 1999 . “ Numerical optimization ” . New York, Inc : Springer-Verlag .
   Google Scholar
• Nocedal , J. 1980 . Updating quasi-Newton matrices with limited storage . Math. Comput. , 35 : 773 – 782 .
   Web of Science ®Google Scholar
• Polyak , B. T. 1987 . “ Introduction to optimization,Optimization Software, Inc. ” . New York : Publications Division .
   Google Scholar
• Penot , J. P. 2002 . On the convergence of descent algorithms . Comput. Optim. Appl. , 23 : 279 – 284 .
   Web of Science ®Google Scholar
• Raydan , M. 1993 . On the Barzilai and Borwein choice of steplength for the gradient method . IMA J. Numer. Anal. , 13 : 321 – 326 .
   Web of Science ®Google Scholar
• Raydan , M. 1997 . The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem . SIAM J. Optim. , 7 ( 1 ) : 26 – 33 .
   Web of Science ®Google Scholar
• Raydan , M. and Svaiter , B. F. 2002 . Relaxed steepest descent and Cauchy-Barzilai-Borwein method . Comput. Optim. Appl. , 21 : 155 – 167 .
   Web of Science ®Google Scholar
• Sun , W. Y. , Han , J. Y. and Sun , J. Global convergence of nonmonotone descent methods for unconstrained optimization problems . Sino-Japan Optimization Meeting . 2000 , Hong Kong. J. Comput. Appl. Math. , Vol. 146 , pp. 89 – 98 .
   Google Scholar
• Shi , Z. J. and Shen , J. 2006 . On memory gradient method with trust region for unconstrained optimization . Numer Algorithms, , 41 : 173 – 196 .
   Web of Science ®Google Scholar
• Shi , Z. J. 2004 . Convergence of multi-step curve search method for unconstrained optimization . J. Numer. Math. , 12 ( 4 ) : 297 – 309 .
   Google Scholar
• Shi , Z. J. 2003 . A new memory gradient method for unconstrained optimization . Asia-Pacific J. Oper. Res. , 20 ( 2 ) : 275 – 284 .
   Google Scholar
• Shi , Z. J. and Shen , J. 2004 . A gradient-related algorithm with inexact line searches . J. Comput. Appl. Math. , 170 : 349 – 370 .
   Web of Science ®Google Scholar
• Wolfe , M. A. and Viazminsky , C. 1976 . Supermemory descent methods for unconstrained optimization . J. Optim. Theory Appl. , 18 ( 4 ) : 455 – 468 .
   Google Scholar
• Yuan , Y. 1993 . “ Numerical Methods for Nonlinear Programming ” . Shanghai Science and Technology Publisher .
   Google Scholar
• Yuan , Y. Subspace techniques for nonlinear optimization . In Proceedings of Shanghai Forum on Industrial and Applied Mathematics , Edited by: Li , D. Q.
   Google Scholar
• Zhu , Z. W. 2002 . A modified trust region algorithm . Optim. Methods Softw. , 17 : 587 – 604 .
   Web of Science ®Google Scholar