A new class of spectral conjugate gradient methods based on a modified secant equation for unconstrained optimization
Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of spectral conjugate gradient methods which ensures sufficient...
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| Published in: | Journal of computational and applied mathematics Vol. 239; pp. 396 - 405 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.02.2013
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of spectral conjugate gradient methods which ensures sufficient descent independent of the accuracy of the line search. Moreover, an attractive property of our proposed methods is that they achieve a high-order accuracy in approximating the second order curvature information of the objective function by utilizing the modified secant condition proposed by Babaie-Kafaki et al. [S. Babaie-Kafaki, R. Ghanbari, N. Mahdavi-Amiri, Two new conjugate gradient methods based on modified secant equations, Journal of Computational and Applied Mathematics 234 (2010) 1374–1386]. Further, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness. |
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| AbstractList | Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of spectral conjugate gradient methods which ensures sufficient descent independent of the accuracy of the line search. Moreover, an attractive property of our proposed methods is that they achieve a high-order accuracy in approximating the second order curvature information of the objective function by utilizing the modified secant condition proposed by Babaie-Kafaki et al. [S. Babaie-Kafaki, R. Ghanbari, N. Mahdavi-Amiri, Two new conjugate gradient methods based on modified secant equations, Journal of Computational and Applied Mathematics 234 (2010) 1374–1386]. Further, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness. Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of spectral conjugate gradient methods which ensures sufficient descent independent of the accuracy of the line search. Moreover, an attractive property of our proposed methods is that they achieve a high-order accuracy in approximating the second order curvature information of the objective function by utilizing the modified secant condition proposed by Babaie-Kafaki et al. [S. Babaie-Kafaki, R. Ghanbari, N. Mahdavi-Amiri, Two new conjugate gradient methods based on modified secant equations, Journal of Computational and Applied Mathematics 234 (2010) 1374-1386]. Further, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness. |
| Author | Livieris, Ioannis E. Pintelas, Panagiotis |
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| Keywords | Line search Modified secant equation Global convergence Spectral conjugate gradient methods Sufficient descent property |
| Language | English |
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| References | Li, Tang, Wei (br000075) 2007; 202 Shi, Guo (br000170) 2009; 224 Shi, Shen (br000175) 2006; 193 Hager, Zhang (br000035) 2006; 2 Powell (br000155) 1977; 12 Hager, Zhang (br000100) 2005; 16 Dolan, Moré (br000115) 2002; 91 Zhang, Xu (br000125) 2001; 137 Raydan (br000145) 2007; 7 Ford, Narushima, Yabe (br000070) 2008; 40 Sun, Han, Sun (br000180) 2002; 146 Ford, Moghrabi (br000055) 1994; 50 Wei, Yu, Yuan, Lian (br000065) 2004; 29 Barzilai, Borwein (br000045) 1988; 8 Yu, Guan, Chen (br000105) 2008; 23 Birgin, Martínez (br000040) 1999; 43 Gilbert, Nocedal (br000140) 1992; 2 Babaie-Kafaki, Fatemi, Mahdavi-Amiri (br000080) 2011; 58 Han, Sun, Sun (br000165) 2002; 146 Fletcher, Reeves (br000010) 1964; 7 Babaie-Kafaki, Ghanbari, Mahdavi-Amiri (br000050) 2010; 234 Xiao, Wang, Wang (br000150) 2010; 234 Dai, Han, Liu, Sun, Yin, Yan (br000135) 1999; 2 G.H. Yu, Nonlinear self-scaling conjugate gradient methods for large-scale optimization problems, Ph.D. Thesis, Sun Yat-Sen University, 2007. Perry (br000020) 1978; 26 Yuan (br000110) 2009; 3 Polak, Ribière (br000015) 1969; 16 Dai, Yuan (br000025) 2000 Ford, Moghrabi (br000060) 1996; 66 Zhang, Deng, Chen (br000120) 1999; 102 Hestenes, Stiefel (br000005) 1952; 49 Zhang, Zhou, Li (br000085) 2006; 104 Zhang, Zhou, Li (br000095) 2007; 22 Nocedal, Wright (br000030) 1999 Grippo, Lucidi (br000160) 1997; 78 Zhang, Zhou, Li (br000090) 2006; 26 10.1016/j.cam.2012.09.007_br000130 Dai (10.1016/j.cam.2012.09.007_br000135) 1999; 2 Polak (10.1016/j.cam.2012.09.007_br000015) 1969; 16 Ford (10.1016/j.cam.2012.09.007_br000060) 1996; 66 Grippo (10.1016/j.cam.2012.09.007_br000160) 1997; 78 Sun (10.1016/j.cam.2012.09.007_br000180) 2002; 146 Barzilai (10.1016/j.cam.2012.09.007_br000045) 1988; 8 Zhang (10.1016/j.cam.2012.09.007_br000085) 2006; 104 Gilbert (10.1016/j.cam.2012.09.007_br000140) 1992; 2 Xiao (10.1016/j.cam.2012.09.007_br000150) 2010; 234 Powell (10.1016/j.cam.2012.09.007_br000155) 1977; 12 Han (10.1016/j.cam.2012.09.007_br000165) 2002; 146 Birgin (10.1016/j.cam.2012.09.007_br000040) 1999; 43 Zhang (10.1016/j.cam.2012.09.007_br000120) 1999; 102 Yu (10.1016/j.cam.2012.09.007_br000105) 2008; 23 Wei (10.1016/j.cam.2012.09.007_br000065) 2004; 29 Shi (10.1016/j.cam.2012.09.007_br000170) 2009; 224 Shi (10.1016/j.cam.2012.09.007_br000175) 2006; 193 Perry (10.1016/j.cam.2012.09.007_br000020) 1978; 26 Li (10.1016/j.cam.2012.09.007_br000075) 2007; 202 Babaie-Kafaki (10.1016/j.cam.2012.09.007_br000080) 2011; 58 Nocedal (10.1016/j.cam.2012.09.007_br000030) 1999 Zhang (10.1016/j.cam.2012.09.007_br000095) 2007; 22 Ford (10.1016/j.cam.2012.09.007_br000070) 2008; 40 Zhang (10.1016/j.cam.2012.09.007_br000090) 2006; 26 Yuan (10.1016/j.cam.2012.09.007_br000110) 2009; 3 Zhang (10.1016/j.cam.2012.09.007_br000125) 2001; 137 Hager (10.1016/j.cam.2012.09.007_br000100) 2005; 16 Dolan (10.1016/j.cam.2012.09.007_br000115) 2002; 91 Fletcher (10.1016/j.cam.2012.09.007_br000010) 1964; 7 Hager (10.1016/j.cam.2012.09.007_br000035) 2006; 2 Hestenes (10.1016/j.cam.2012.09.007_br000005) 1952; 49 Dai (10.1016/j.cam.2012.09.007_br000025) 2000 Ford (10.1016/j.cam.2012.09.007_br000055) 1994; 50 Babaie-Kafaki (10.1016/j.cam.2012.09.007_br000050) 2010; 234 Raydan (10.1016/j.cam.2012.09.007_br000145) 2007; 7 |
| References_xml | – volume: 91 start-page: 201 year: 2002 end-page: 213 ident: br000115 article-title: Benchmarking optimization software with performance profiles publication-title: Mathematical Programming – volume: 26 start-page: 629 year: 2006 end-page: 640 ident: br000090 article-title: A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence publication-title: IMA Journal of Numerical Analysis – volume: 234 start-page: 2986 year: 2010 end-page: 2992 ident: br000150 article-title: Notes on the Dai–Yuan–Yuan modified spectral gradient method publication-title: Journal of Computational and Applied Mathematics – volume: 146 start-page: 89 year: 2002 end-page: 98 ident: br000165 article-title: Global convergence of non-monotone descent methods for unconstrained optimization problems publication-title: Journal of Computational and Applied Mathematics – volume: 193 start-page: 397 year: 2006 end-page: 412 ident: br000175 article-title: Convergence of nonmonotone line search method publication-title: Journal of Computational and Applied Mathematics – volume: 78 start-page: 375 year: 1997 end-page: 391 ident: br000160 article-title: A globally convergent version of the Polak–Ribière conjugate gradient method publication-title: Mathematical Programming – volume: 234 start-page: 1374 year: 2010 end-page: 1386 ident: br000050 article-title: Two new conjugate gradient methods based on modified secant equations publication-title: Journal of Computational and Applied Mathematics – volume: 8 start-page: 141 year: 1988 end-page: 148 ident: br000045 article-title: Two point step size gradient methods publication-title: IMA Journal of Numerical Analysis – volume: 3 start-page: 11 year: 2009 end-page: 21 ident: br000110 article-title: Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems publication-title: Optimization Letters – volume: 16 start-page: 170 year: 2005 end-page: 192 ident: br000100 article-title: A new conjugate gradient method with guaranteed descent and an efficient line search publication-title: SIAM of Journal Optimization – volume: 26 start-page: 1073 year: 1978 end-page: 1078 ident: br000020 article-title: A modified conjugate gradient algorithm publication-title: Operational Research – volume: 202 start-page: 523 year: 2007 end-page: 539 ident: br000075 article-title: New conjugacy condition and related new conjugate gradient methods for unconstrained optimization publication-title: Journal of Computational and Applied Mathematics – volume: 137 start-page: 269 year: 2001 end-page: 278 ident: br000125 article-title: Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equations publication-title: Journal of Computational and Applied Mathematics – year: 1999 ident: br000030 article-title: Numerical Optimization – volume: 43 start-page: 117 year: 1999 end-page: 128 ident: br000040 article-title: A spectral conjugate gradient method for unconstrained optimization publication-title: Applied Mathematics and Optimization – volume: 58 start-page: 315 year: 2011 end-page: 331 ident: br000080 article-title: Two effective hybrid conjugate gradient algorithms based on modified BFGS updates publication-title: Numerical Algorithms – reference: G.H. Yu, Nonlinear self-scaling conjugate gradient methods for large-scale optimization problems, Ph.D. Thesis, Sun Yat-Sen University, 2007. – volume: 16 start-page: 35 year: 1969 end-page: 43 ident: br000015 article-title: Note sur la convergence de methods de directions conjuguees publication-title: Revue Francais d’Informatique et de Recherche Operationnelle – volume: 12 start-page: 241 year: 1977 end-page: 254 ident: br000155 article-title: Restart procedures for the conjugate gradient method publication-title: Mathematical Programming – volume: 2 start-page: 345 year: 1999 end-page: 358 ident: br000135 article-title: Convergence properties of nonlinear conjugate gradient methods publication-title: SIAM Journal of Optimization – volume: 2 start-page: 21 year: 1992 end-page: 42 ident: br000140 article-title: Global convergence properties of conjugate gradient methods for optimization publication-title: SIAM Journal of Optimization – volume: 23 start-page: 275 year: 2008 end-page: 293 ident: br000105 article-title: Spectral conjugate gradient methods with sufficient descent property for large-scale unconstrained optimization publication-title: Optimization Methods and Software – volume: 50 start-page: 305 year: 1994 end-page: 323 ident: br000055 article-title: Multi-step quasi-Newton methods for optimization publication-title: Journal of Computational and Applied Mathematics – volume: 2 start-page: 35 year: 2006 end-page: 58 ident: br000035 article-title: A survey of nonlinear conjugate gradient methods publication-title: Pacific of Journal Optimization – volume: 40 start-page: 191 year: 2008 end-page: 216 ident: br000070 article-title: Multi-step nonlinear conjugate gradient methods for unconstrained minimization publication-title: Computational Optimization and Applications – volume: 7 start-page: 149 year: 1964 end-page: 154 ident: br000010 article-title: Function minimization by conjugate gradients publication-title: Computer Journal – volume: 146 start-page: 89 year: 2002 end-page: 98 ident: br000180 article-title: Global convergence of nonmonotone descent methods for unconstrained optimization problems publication-title: Journal of Computational and Applied Mathematics – volume: 66 start-page: 201 year: 1996 end-page: 211 ident: br000060 article-title: Using function-values multi-step quasi-Newton methods publication-title: Journal of Computational and Applied Mathematics – volume: 102 start-page: 147 year: 1999 end-page: 167 ident: br000120 article-title: New quasi-Newton equation and related methods for unconstrained optimization publication-title: Journal of Optimization Theory and Applications – volume: 29 start-page: 315 year: 2004 end-page: 332 ident: br000065 article-title: The superlinear convergence of a modified BFGS-type method for unconstrained optimization publication-title: Computational Optimization and Applications – volume: 224 start-page: 444 year: 2009 end-page: 457 ident: br000170 article-title: A new family of conjugate gradient methods publication-title: Journal of Computational and Applied Mathematics – volume: 22 start-page: 697 year: 2007 end-page: 711 ident: br000095 article-title: Some descent three-term conjugate gradient methods and their global convergence publication-title: Optimization Methods and Software – volume: 104 start-page: 561 year: 2006 end-page: 572 ident: br000085 article-title: Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search publication-title: Numerische Mathematik – volume: 7 start-page: 26 year: 2007 end-page: 33 ident: br000145 article-title: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem publication-title: SIAM Journal of Optimization – year: 2000 ident: br000025 article-title: Nonlinear Conjugate Gradient Methods – volume: 49 start-page: 409 year: 1952 end-page: 436 ident: br000005 article-title: Methods for conjugate gradients for solving linear systems publication-title: Journal of Research of the National Bureau of Standards – volume: 22 start-page: 697 year: 2007 ident: 10.1016/j.cam.2012.09.007_br000095 article-title: Some descent three-term conjugate gradient methods and their global convergence publication-title: Optimization Methods and Software doi: 10.1080/10556780701223293 – volume: 146 start-page: 89 issue: 2 year: 2002 ident: 10.1016/j.cam.2012.09.007_br000180 article-title: Global convergence of nonmonotone descent methods for unconstrained optimization problems publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/S0377-0427(02)00420-X – year: 2000 ident: 10.1016/j.cam.2012.09.007_br000025 – volume: 16 start-page: 170 year: 2005 ident: 10.1016/j.cam.2012.09.007_br000100 article-title: A new conjugate gradient method with guaranteed descent and an efficient line search publication-title: SIAM of Journal Optimization doi: 10.1137/030601880 – volume: 7 start-page: 149 year: 1964 ident: 10.1016/j.cam.2012.09.007_br000010 article-title: Function minimization by conjugate gradients publication-title: Computer Journal doi: 10.1093/comjnl/7.2.149 – volume: 23 start-page: 275 issue: 2 year: 2008 ident: 10.1016/j.cam.2012.09.007_br000105 article-title: Spectral conjugate gradient methods with sufficient descent property for large-scale unconstrained optimization publication-title: Optimization Methods and Software doi: 10.1080/10556780701661344 – volume: 8 start-page: 141 year: 1988 ident: 10.1016/j.cam.2012.09.007_br000045 article-title: Two point step size gradient methods publication-title: IMA Journal of Numerical Analysis doi: 10.1093/imanum/8.1.141 – volume: 66 start-page: 201 year: 1996 ident: 10.1016/j.cam.2012.09.007_br000060 article-title: Using function-values multi-step quasi-Newton methods publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/0377-0427(95)00178-6 – volume: 224 start-page: 444 issue: 1 year: 2009 ident: 10.1016/j.cam.2012.09.007_br000170 article-title: A new family of conjugate gradient methods publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2008.05.012 – volume: 50 start-page: 305 year: 1994 ident: 10.1016/j.cam.2012.09.007_br000055 article-title: Multi-step quasi-Newton methods for optimization publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/0377-0427(94)90309-3 – volume: 16 start-page: 35 year: 1969 ident: 10.1016/j.cam.2012.09.007_br000015 article-title: Note sur la convergence de methods de directions conjuguees publication-title: Revue Francais d’Informatique et de Recherche Operationnelle – volume: 58 start-page: 315 issue: 3 year: 2011 ident: 10.1016/j.cam.2012.09.007_br000080 article-title: Two effective hybrid conjugate gradient algorithms based on modified BFGS updates publication-title: Numerical Algorithms doi: 10.1007/s11075-011-9457-6 – volume: 26 start-page: 629 issue: 4 year: 2006 ident: 10.1016/j.cam.2012.09.007_br000090 article-title: A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence publication-title: IMA Journal of Numerical Analysis doi: 10.1093/imanum/drl016 – volume: 78 start-page: 375 issue: 3 year: 1997 ident: 10.1016/j.cam.2012.09.007_br000160 article-title: A globally convergent version of the Polak–Ribière conjugate gradient method publication-title: Mathematical Programming doi: 10.1007/BF02614362 – volume: 40 start-page: 191 year: 2008 ident: 10.1016/j.cam.2012.09.007_br000070 article-title: Multi-step nonlinear conjugate gradient methods for unconstrained minimization publication-title: Computational Optimization and Applications doi: 10.1007/s10589-007-9087-z – volume: 234 start-page: 1374 year: 2010 ident: 10.1016/j.cam.2012.09.007_br000050 article-title: Two new conjugate gradient methods based on modified secant equations publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2010.01.052 – volume: 2 start-page: 35 year: 2006 ident: 10.1016/j.cam.2012.09.007_br000035 article-title: A survey of nonlinear conjugate gradient methods publication-title: Pacific of Journal Optimization – year: 1999 ident: 10.1016/j.cam.2012.09.007_br000030 – volume: 29 start-page: 315 year: 2004 ident: 10.1016/j.cam.2012.09.007_br000065 article-title: The superlinear convergence of a modified BFGS-type method for unconstrained optimization publication-title: Computational Optimization and Applications doi: 10.1023/B:COAP.0000044184.25410.39 – volume: 12 start-page: 241 year: 1977 ident: 10.1016/j.cam.2012.09.007_br000155 article-title: Restart procedures for the conjugate gradient method publication-title: Mathematical Programming doi: 10.1007/BF01593790 – volume: 137 start-page: 269 year: 2001 ident: 10.1016/j.cam.2012.09.007_br000125 article-title: Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equations publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/S0377-0427(00)00713-5 – volume: 202 start-page: 523 year: 2007 ident: 10.1016/j.cam.2012.09.007_br000075 article-title: New conjugacy condition and related new conjugate gradient methods for unconstrained optimization publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2006.03.005 – volume: 7 start-page: 26 year: 2007 ident: 10.1016/j.cam.2012.09.007_br000145 article-title: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem publication-title: SIAM Journal of Optimization doi: 10.1137/S1052623494266365 – ident: 10.1016/j.cam.2012.09.007_br000130 – volume: 102 start-page: 147 year: 1999 ident: 10.1016/j.cam.2012.09.007_br000120 article-title: New quasi-Newton equation and related methods for unconstrained optimization publication-title: Journal of Optimization Theory and Applications doi: 10.1023/A:1021898630001 – volume: 2 start-page: 345 year: 1999 ident: 10.1016/j.cam.2012.09.007_br000135 article-title: Convergence properties of nonlinear conjugate gradient methods publication-title: SIAM Journal of Optimization – volume: 146 start-page: 89 year: 2002 ident: 10.1016/j.cam.2012.09.007_br000165 article-title: Global convergence of non-monotone descent methods for unconstrained optimization problems publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/S0377-0427(02)00420-X – volume: 26 start-page: 1073 year: 1978 ident: 10.1016/j.cam.2012.09.007_br000020 article-title: A modified conjugate gradient algorithm publication-title: Operational Research doi: 10.1287/opre.26.6.1073 – volume: 104 start-page: 561 year: 2006 ident: 10.1016/j.cam.2012.09.007_br000085 article-title: Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search publication-title: Numerische Mathematik doi: 10.1007/s00211-006-0028-z – volume: 91 start-page: 201 year: 2002 ident: 10.1016/j.cam.2012.09.007_br000115 article-title: Benchmarking optimization software with performance profiles publication-title: Mathematical Programming doi: 10.1007/s101070100263 – volume: 49 start-page: 409 year: 1952 ident: 10.1016/j.cam.2012.09.007_br000005 article-title: Methods for conjugate gradients for solving linear systems publication-title: Journal of Research of the National Bureau of Standards doi: 10.6028/jres.049.044 – volume: 234 start-page: 2986 issue: 10 year: 2010 ident: 10.1016/j.cam.2012.09.007_br000150 article-title: Notes on the Dai–Yuan–Yuan modified spectral gradient method publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2010.04.012 – volume: 193 start-page: 397 issue: 2 year: 2006 ident: 10.1016/j.cam.2012.09.007_br000175 article-title: Convergence of nonmonotone line search method publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2005.06.033 – volume: 43 start-page: 117 year: 1999 ident: 10.1016/j.cam.2012.09.007_br000040 article-title: A spectral conjugate gradient method for unconstrained optimization publication-title: Applied Mathematics and Optimization doi: 10.1007/s00245-001-0003-0 – volume: 2 start-page: 21 issue: 1 year: 1992 ident: 10.1016/j.cam.2012.09.007_br000140 article-title: Global convergence properties of conjugate gradient methods for optimization publication-title: SIAM Journal of Optimization doi: 10.1137/0802003 – volume: 3 start-page: 11 year: 2009 ident: 10.1016/j.cam.2012.09.007_br000110 article-title: Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems publication-title: Optimization Letters doi: 10.1007/s11590-008-0086-5 |
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| SubjectTerms | Computation Conjugate gradient method Convergence Curvature Global convergence Line search Mathematical analysis Mathematical models Modified secant equation Optimization Searching Spectral conjugate gradient methods Sufficient descent property |
| Title | A new class of spectral conjugate gradient methods based on a modified secant equation for unconstrained optimization |
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