swMATH ID: 5140
Software Authors: Nash, Stephen G.
Description: Newton-type minimization via the Lanczos method This paper discusses the use of the linear conjugate-gradient method (developed via the Lanczos method) in the solution of large-scale unconstrained minimization problems. It is shown how the equivalent Lanczos characterization of the linear conjugate-gradient method may be exploited to define a modified Newton method which can be applied to problems that do not necessarily have positive-definite Hessian matrices. This derivation also makes it possible to compute a negative-curvature direction at a stationary point. The above mentioned modified Lanczos algorithm requires up to n iterations to compute the search direction, where n denotes the number of variables of the problem. The idea of a truncated Newton method is to terminate the iterations earlier. A preconditioned truncated Newton method is described that defines a search direction which interpolates between the direction defined by a nonlinear conjugate-gradient-type method and a modified Newton direction. Numerical results are given which show the promising performance of truncated Newton methods.
Homepage: http://www.netlib.org/opt/tn
Programming Languages: C
Keywords: linear conjugate-gradient method; Lanczos method; large-scale unconstrained minimization; negative-curvature direction; preconditioned truncated Newton method; Numerical results
Related Software: L-BFGS; CUTEr; TNPACK; minpack; LANCELOT; KELLEY; ve08; TRON; GQTPAR; PREQN; CUTE; Algorithm 500; LBFGS-B; CUTEst; HSL-VF05; L-BFGS-B; HSL; mctoolbox; SifDec; SeDuMi
Referenced in: 140 Publications
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Referenced by 237 Authors

11 Fasano, Giovanni
11 Roma, Massimo
7 Nash, Stephen G.
6 Navon, Ionel Michael
5 Andrei, Neculai
4 Martínez, José Mario
4 Nocedal, Jorge
4 Plecháč, Petr
4 Wei, Zengxin
3 Caliciotti, Andrea
3 Carstensen, Carsten
3 Deng, Naiyang
3 Di, Zichao
3 Kojima, Masakazu
3 Lucidi, Stefano
3 Schlick, Tamar
3 Spellucci, Peter
3 Yuan, Gonglin
3 Zhang, Jianzhong
2 Brossier, Romain
2 Daescu, Dacian N.
2 de Hoog, Frank Robert
2 Gill, Philip E.
2 Gratton, Serge
2 Grote, Marcus J.
2 Kim, Sunyoung
2 Le Dimet, Francois-Xavier
2 Leyffer, Sven
2 Mercier, Sylvain
2 Morales, José Luis
2 Nahum, Uri
2 O’Leary, Dianne P.
2 Operto, Stéphane
2 Pesenti, Raffaele
2 Tardieu, Nicolas
2 Toint, Philippe L.
2 Vasseur, Xavier
2 Virieux, Jean
2 Wang, Zhi
2 Wild, Stefan M.
2 Xu, Chengxian
2 Xue, Guoliang
2 Zhou, Bojian
2 Zibulevsky, Michael
1 Abdel-Aziz, Mohammedi R.
1 Ahmed, A. I.
1 Akrotirianakis, Ioannis G.
1 Al-Baali, Mehiddin
1 Al-Haik, M. S.
1 Alekseev, Aleksey K.
1 Anderssen, Robert Scott
1 Antil, Harbir
1 Armand, Paul
1 Austin, Anthony P.
1 Balaras, Elias
1 Bank, Randolph E.
1 Bao, Michael
1 Benoist, Joël
1 Bliemer, Michiel C. J.
1 Borthwick, Alistair G. L.
1 Borzì, Alfio
1 Boyd, Stephen Poythress
1 Brás, Carmo P.
1 Bronstein, Alexander M.
1 Bronstein, Michael M.
1 Browne, Edward P.
1 Busseti, Enzo
1 Byers, Ralph
1 Byrd, Richard H.
1 Campos, Juan S.
1 Chakraborty, Suvra Kanti
1 Chang, Haw-Shiuan
1 Chelikowsky, James R.
1 Chen, Chunhui
1 Cheng, Bin
1 Cheung, Ying Kuen K.
1 Chin, Gillian M.
1 Chouzenoux, Emilie
1 Chung, Julianne M.
1 Chung, Peter W.
1 Curtis, Frank E.
1 Cushman, John H.
1 Dai, Yu-Hong
1 Daydé, Michel J.
1 De Leone, Renato
1 De Simone, Valentina
1 Demmel, James Weldon
1 di Serafino, Daniela
1 Di, Zichao Wendy
1 Droegemeier, Kelvin K.
1 Duan, Xiabin
1 Dussault, Jean-Pierre
1 El-Alem, Mahmoud M.
1 Erway, Jennifer B.
1 Fedkiw, Ronald P.
1 Ferris, Michael C.
1 Fliege, Jörg
1 Fogelson, Aaron L.
1 Fosdick, Roger L.
1 Freddi, Francesco
...and 137 more Authors
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Referenced in 64 Serials

17 Computational Optimization and Applications
10 SIAM Journal on Optimization
8 Journal of Optimization Theory and Applications
6 Journal of Computational and Applied Mathematics
6 Optimization Methods & Software
5 Journal of Global Optimization
4 Mathematical Programming. Series A. Series B
4 SIAM Journal on Scientific Computing
3 International Journal for Numerical Methods in Fluids
3 Inverse Problems
3 SIAM Journal on Imaging Sciences
2 Computers and Fluids
2 Computers & Mathematics with Applications
2 Computer Methods in Applied Mechanics and Engineering
2 Journal of Computational Physics
2 Mathematics of Computation
2 ACM Transactions on Mathematical Software
2 Numerical Functional Analysis and Optimization
2 SIAM Journal on Numerical Analysis
2 Numerical Algorithms
2 Applied Mathematical Modelling
2 SIAM Review
2 Numerical Linear Algebra with Applications
1 IMA Journal of Numerical Analysis
1 Journal of Fluid Mechanics
1 Journal of Statistical Physics
1 Mathematical Methods in the Applied Sciences
1 Applied Mathematics and Computation
1 Applied Mathematics and Optimization
1 Computing
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1 International Journal of Mathematics and Mathematical Sciences
1 Journal of the American Statistical Association
1 Journal of the Korean Mathematical Society
1 Mathematics and Computers in Simulation
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1 SIAM Journal on Scientific and Statistical Computing
1 Journal of Information & Optimization Sciences
1 Operations Research Letters
1 Applied Numerical Mathematics
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1 Algorithmica
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1 Mathematical and Computer Modelling
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1 Science in China. Series A
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1 Journal of Statistical Computation and Simulation
1 Linear Algebra and its Applications
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1 Boletín de la Sociedad Matemática Mexicana. Third Series
1 Mathematical Problems in Engineering
1 International Journal of Computational Fluid Dynamics
1 Abstract and Applied Analysis
1 Vychislitel’nye Tekhnologii
1 Chaos
1 Journal of Machine Learning Research (JMLR)
1 Journal of Applied Mathematics and Computing
1 Acta Numerica
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