[1] Barzilai J, Borwein J. Two-point step size gradient methods[J]. IMA J Numer Anal, 1988, 8: 141-148.[2] Raydan M, Svziter B F. Relaxed steepest descent and Cauchy-Barzilai-Borwein method[J]. Com-put Optim Appl, 2002, 21:155-167.[3] Dai Y H, Liao L Z. R-linear convergence of the Barzilai and Borwein gradient method[J]. IMA J Numer Anal, 2002, 22(1):1-10.[4] Raydan M. On The Barzilai and Borwein choice of steplength for the gradient method[J]. IMA J Numer Anal, 1993, 13:321-326.[5] Dai Y H, Yuan J Y, Yuan Y Y. Modified two-point stepsize gradient methods for unconstrained optimization[J]. Comput Optim and Appl, 2002, 22:103-109.[6] Dai Y H, Alternate step gradient Method[J]. Optim, 2003, 52(4-5),395-415.[7] Dai Y H,Yuan Y X, Alternate minimization gradient method[J]. IMA J Numer Anal, 2003, 23:377-393.[8] Grippo L, Sciandrone M. Nonmonotone globalization techniques for the Barzilai-Borwein gradient method[J]. Comput Optim and Appl, 2002, 23:143-169.[9] Dai Y H, Roger F. Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming[J]. Numer Math, 2005, 100(1):21-47.[10] Friedlander A, Martinez J, Molina B, Raydan M. Gradient method with retards and generaliza-tions[J]. SIAM J Numer Anal, 1999, 36:275-289.[11] Lamotte J L, Molina B, Raydan M. Smooth and adaptive gradient method with retards[J]. Math Comput Model, 2006, 36(9-10):1161-1168.[12] Dai Y H, Yuan Y. Analyses of monotone gradient methods[J]. Ind Manag Optim, 2005, 1:181-192.[13] Yuan Y. A new stepsize for the steepest descent method[J]. Comp Math, 2006, 24:149-156.[14] Yuan Y. Step-sizes for the gradient method[G]. in:K S Liu, Z P Xin and S T Yau, eds, Third International Congress of Chinese Mathematicians(AMS/IP Studies in Advanced Mathematics), 42(2):785-796.[15] Fletcher R. A limited memory steepest descent method[J]. Math Program, 2012, 135:413-436.[16] Roberta D A, Daniela d S, Filippo R, Gerardo T. On spectral properties of steepest descent methods[J]. IMA J Numer Anal, 2013, 33:1416-1435.[17] 袁亚湘. 信赖域方法的收敛性[J]. 计算数学, 1994, 08(3):333-346.[18] 孙文瑜, 徐贤成, 朱德通. 最优化方法[M]. 北京:高等教育出版社, 2011.[19] Yuan Y. On the truncated conjugate gradient method[J]. Math Program, 2000, 87:561-571.[20] 李正锋, 邓乃扬. 一类新的非单调信赖域算法及其收敛性[J]. 应用数学学报, 1999, 22(3):457-465.[21] Chen J, Sun W Y. Nonmonotone Adaptivee Trust Region Algorithms with Indefinite Dogleg Path for Unconstrained Minimization[J]. Northeast Math, 2008, 24(1):19-30.[22] Bastin F, Malmedy V, Mouffe M, Toint Ph L, et al. A Retrospective Trust-Region Method for Unconstrained Optimization[J]. Math Program, 2010, 123(2):395-418.[23] Cartis C, Gould N I M, Toint Ph L. Adaptive cubic overestimation methods for unconstrained optimization[J]. Math Program, 2011, 130(2):295-319.[24] 戴彧虹, 刘新为. 线性与非线性规划算法与理论[J]. 运筹学学报, 2014, 18(1):69-92.[25] Raydan M. Convergence properties of the Barzilai and Borwein gradient method[D]. USA:Rice University, 1991.[26] Roberta D A, Daniela d S, Gerardo T. An efficient gradient method using the Yuan steplength[J]. Comput Optim Appl, 2014, 59:541-563. |