New Hybrid Conjugate Gradient Method As A Convex Combination of Ls and Fr Methods
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Al-Baali M. Descent property and global convergence of the Fletcher-Reeves method with inexact line search. IMA J Numer Anal, 1985, 5: 121–124
Andrei N. New hybrid conjugate gradient algorithms for unconstrained optimization. Encyclopedia of Optimization, 2009: 2560–2571
Andrei N. A hybrid conjugate gradient algorithm with modified secant condition for unconstrained optimization as a convex combination of Hestenes-Stiefel and Dai-Yuan algorithms. Studies in Informatics and Control, 2008, 17(4): 373–392
Andrei N. A hybrid conjugate gradient algorithm for unconstrained optimization as a convex combination of Hestenes-Stiefel and Dai-Yuan. Studies in Informatics and Control, 2008, 17(1): 55–70
Andrei N. Another hybrid conjugate gradient algorithm for unconstrained optimization. Numerical Algorithms, 2008, 47(2): 143–156
Andrei N. An unconstrained optimization test functions. Advanced Modeling and Optimization, An Electronic International Journal, 2008, 10: 147–161
Andrei N. Accelerated hybrid conjugate gradient algorithm with modified secant condition for unconstrained optimization. Numer Algorithms, 2010, 54: 23–46
Dai Y H, Yuan Y. Convergence properties of the Fletcher-Reeves method. IMA J Numer Anal, 1996, 16: 155–164
Dai Y H, Liao L Z. New conjugacy conditions and related nonlinear conjugate gradient methods. Appl Math Optim, 2001, 43: 87–101
Dai Y H, Yuan Y. A nonlinear conjugate gradient method with a strong global convergence property. SIAM J Optim, 1999, 10: 177–182
Dai Y H, Han J Y, Liu G H, Sun D F, Yin X, Yuan Y. Convergence properties of nonlinear conjugate gradient methods. SIAM J Optim, 1999, 10: 348–358
Dai Y H. A family of hybrid conjugate gradient methods for unconstrained optimization. Math Comp, 2003, 72: 1317–1328
Dai Y H, Yuan Y. A class of globally convergent conjugate gradient methods. Sci China Ser A, 2003, 46: 251–262
Đorđević S S. New hybrid conjugate gradient method as a convex combination of FR and PRP methods. Filomat, 2016, 30(11): 3083–3100
Dolan E D, Moré J J. Benchmarking optimization software with performance profiles. Math Programming, 2002, 91: 201–213
Fletcher R. Practical Methods of Optimization Vol. 1: Unconstrained Optimization. New York: John Wiley and Sons, 1987
Gilbert J C, Nocedal J. Global convergence properties of conjugate gradient methods for optimization. SIAM J Optim, 1992, 2: 21–42
Hager W W, Zhang H. A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J Optim, 2003, 16(1): 170–192
Hager W W, Zhang H. CG-DESCENT, a conjugate gradient method with guaranteed descent. ACM Transactions on Mathematical Software, 2006, 32(1): 113–137
Hager W W, Zhang H. A survey of nonlinear conjugate gradient methods. Pacific J Optim, 2006, 2: 35–58
Hestenes M R, Stiefel E L. Methods of conjugate gradients for solving linear systems. J Research Nat Bur Standards, 1952, 49: 409–436
Hu Y F, Storey C. Global convergence result for conjugate gradient methods. J Optim Theory Appl, 1991, 71: 399–405
Liu J K, Li S J. New hybrid conjugate gradient method for unconstrained optimization. Appl Math Comput, 2014, 245: 36–43
Liu Y, Storey C. Efficient generalized conjugate gradient algorithms, part 1: theory. JOTA, 1991, 69: 129–137
Liu G H, Han J Y, Yin H X. Global convergence of the Fletcher-Reeves algorithm with an inexact line search. Appl Math J Chinese Univ, Ser B, 1995, 10: 75–82
Polak E, Ribiére G. Note sur la convergence de méthodes de directions conjugués. Revue Fran¸caise d’Informatique et de Recherche Opérationnelle, 1969, 16: 35–43
Polyak B T. The conjugate gradient method in extreme problems. USSR Comp Math Math Phys, 1969, 9: 94–112
Touati-Ahmed D, Storey C. Efficient hybrid conjugate gradient techniques. J Optim Theory Appl, 1990, 64: 379–397
Wolfe P. Convergence conditions for ascent methods. II: Some corrections. SIAM Review, 1969, 11: 226–235
Yang X, Luo Z, Dai X. A global convergence of LS-CD hybrid conjugate gradient method. Adv Numer Anal, 2013, 2013: Article ID 517452, 5 pages
Yuan Y, Stoer J. A subspace study on conjugate gradient algorithm. Z Angew Math Mech, 1995, 75: 69–77
Yuan G, Meng Z, Li Y. A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations. J Optim Theory Appl, 2016, 168: 129–152
Yuan G, Wei Z, Li G. A modified Polak-Ribi`ere-Polyak conjugate gradient algorithm for nonsmooth convex programs. J Comput Appl Math, 2014, 255: 86–96
Yuan G, Wei Z, Lu X. Global convergence of BFGS and PRP methods under a modified weak Wolfe-Powell line search. Appl Math Model, 2017, 47: 811–825
Yuan G, Wei Z, Zhao Q. A modified Polak-Ribiére-Polyak conjugate gradient algorithm for large-scale optimization problems. IIE Transactions, 2014, 46: 397–413
Yuan G, Zhang M. A three-terms Polak-Ribiére-Polyak conjugate gradient algorithm for large-scale nonlinear equations. J Comput Appl Math, 2015, 286: 186–195
Zoutendijk G. Nonlinear programming, computational methods// Abadie J, ed. Integer and Nonlinear Programming. Amsterdam: North-Holland, 1970: 37–86