## L-BFGS-B

 swMATH ID: 1234 Software Authors: Ciyou Zhu, Richard Byrd, Jorge Nocedal, Jose Luis Morales Description: Algorithm 778: L-BFGS-B Fortran subroutines for large-scale bound-constrained optimization. L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be used for unconstrained problems and in this case performs similarly to its predecessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemened in Fortran 77. Homepage: http://users.eecs.northwestern.edu/~nocedal/lbfgsb.html Keywords: arge scale optimization; variable metric method; limited-memory algorithm; large nonlinear optimization problems Related Software: L-BFGS; LBFGS-B; CUTEr; TRON; LANCELOT; SNOPT; Ipopt; SciPy; R; SifDec; KELLEY; GitHub; TAPENADE; CUTE; SPG; Matlab; Adam; MINOS; CG_DESCENT; GALAHAD Cited in: 196 Publications
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### Cited by 476 Authors

 6 Nocedal, Jorge 6 Sandu, Adrian 5 Herty, Michael Matthias 4 Klar, Axel 3 Birgin, Ernesto G. 3 Brust, Johannes J. 3 Byrd, Richard H. 3 Cioaca, Alexandru 3 Hager, William W. 3 Hanifi, Ardeshir 3 Orban, Dominique 3 Pralits, Jan Oscar 3 Shen, Chunhua 3 Xiao, Yunhai 3 Zhang, Hongchao 2 Aanonsen, Sigurd Ivar 2 Alexe, Mihai 2 Avellaneda, Marco 2 Borges, Patrick 2 Brunton, Steven L. 2 Buff, Robert 2 Dharmavaram, Sanjay 2 Egidi, Nadaniela 2 Eydinov, Dmitry 2 Fourestey, Gilles 2 Friedman, Craig 2 Gill, Philip E. 2 Gould, Nicholas Ian Mark 2 Groenwold, Albert A. 2 Henningson, Dan S. 2 Kanzow, Christian 2 Klug, Andreas 2 Krislock, Nathan 2 Kurbatsky, Victor Grigorevich 2 Kutz, J. Nathan 2 Leyffer, Sven 2 Lin, Chih-Jen 2 Malick, Jérôme 2 Maponi, Pierluigi 2 Marcia, Roummel F. 2 Martínez, José Mario 2 Mavriplis, Dimitri J. 2 Mei, Yue 2 Morales, José Luis 2 Müller, Jens-Dominik 2 Osher, Stanley Joel 2 Persson, Per-Olof 2 Petra, Cosmin G. 2 Pytlak, Radosław 2 Roupin, Frédéric 2 Rudy, Samuel H. 2 Rumpfkeil, Markus P. 2 Saunders, Michael A. 2 Sidorov, Denis Nikolaevich 2 Spellucci, Peter 2 Spiryaev, Vadim Aleksandrovich 2 Toint, Philippe L. 2 Tomin, Nikita Viktorovich 2 van den Hengel, Anton 2 Waltz, Richard A. 2 Wei, Zengxin 2 Womersley, Robert S. 2 Zahr, Matthew J. 2 Zhu, Ciyou 2 Zingg, David W. 1 Aavatsmark, Ivar 1 Abarbanel, Henry D. I. 1 Abellan, A. 1 Addessi, Daniela 1 Aggarwal, Ankush 1 Airiau, Christophe 1 Akhriev, Albert 1 Albert, Christopher G. 1 Alexanderian, Alen 1 Ammar, Haitham Bou 1 Andreani, Roberto 1 Aquino, Wilkins 1 Auriemma, Salvatore 1 Baghfalaki, Taban 1 Balaras, Elias 1 Banerjee, Biswanath 1 Banović, Mladen 1 Barabasz, Barbara 1 Bardsley, Johnathan M. 1 Baydin, Atılım Güneş 1 Bayer, Fábio Mariano 1 Beaulieu, François D. 1 Becker, Stephen R. 1 Beierle, Christoph 1 Benešová, Barbora 1 Bianchi, Pascal 1 Bientinesi, Paolo 1 Bischl, Bernd 1 Bisognin, Cleber 1 Bolton, Hermanus P. J. 1 Bonneel, Nicolas 1 Bonnet, Marc 1 Borthwick, Alistair G. L. 1 Bostanabad, Ramin 1 Bouchnita, Anass ...and 376 more Authors
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### Cited in 88 Serials

 13 Computer Methods in Applied Mechanics and Engineering 13 Journal of Computational Physics 12 SIAM Journal on Optimization 12 Computational Optimization and Applications 6 ACM Transactions on Mathematical Software 5 Computers and Fluids 5 Machine Learning 5 SIAM Journal on Scientific Computing 4 Inverse Problems 4 Optimization Methods & Software 4 Optimization and Engineering 3 Computers & Mathematics with Applications 3 Journal of Optimization Theory and Applications 3 Numerische Mathematik 3 Mathematical Programming. Series A. Series B 3 International Journal of Computer Vision 3 Computational Geosciences 3 Mathematical Geosciences 2 Journal of Fluid Mechanics 2 Applied Mathematics and Computation 2 Journal of Computational and Applied Mathematics 2 Mathematics and Computers in Simulation 2 Journal of Global Optimization 2 Applied Mathematical Modelling 2 Journal of Mathematical Imaging and Vision 2 Mathematical Problems in Engineering 2 Chaos 2 Journal of Applied Statistics 2 Quantitative Finance 2 Journal of Machine Learning Research (JMLR) 1 Journal of Mathematical Analysis and Applications 1 Scandinavian Journal of Statistics 1 Mathematics of Computation 1 Bulletin of Mathematical Biology 1 Acta Cybernetica 1 Information Sciences 1 Journal of Statistical Planning and Inference 1 Applied Numerical Mathematics 1 Computers & Operations Research 1 Computational Mechanics 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Scientific Computing 1 Neural Networks 1 Signal Processing 1 Neural Computation 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Computational Statistics 1 Automation and Remote Control 1 European Journal of Operational Research 1 SIAM Review 1 Computational Statistics and Data Analysis 1 Physics of Fluids 1 Applied Mathematical Finance 1 Discrete and Continuous Dynamical Systems 1 Nonlinear Dynamics 1 Abstract and Applied Analysis 1 Vychislitel’nye Tekhnologii 1 Mathematical Methods of Operations Research 1 International Journal of Theoretical and Applied Finance 1 Flow, Turbulence and Combustion 1 Communications in Nonlinear Science and Numerical Simulation 1 International Journal of Applied Mathematics and Computer Science 1 CEJOR. Central European Journal of Operations Research 1 Combustion Theory and Modelling 1 The ANZIAM Journal 1 Statistical Modelling 1 Quantum Information Processing 1 Structural and Multidisciplinary Optimization 1 Journal of Applied Logic 1 Acta Numerica 1 Computational Management Science 1 Journal of Computational Acoustics 1 Journal of Statistical Mechanics: Theory and Experiment 1 Communications in Computational Physics 1 AStA. Advances in Statistical Analysis 1 SIAM Journal on Imaging Sciences 1 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie 1 Journal of Computational and Graphical Statistics 1 The Journal of Mathematical Neuroscience 1 Journal of Mathematics in Industry 1 Information and Inference 1 Journal of Theoretical Biology 1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 1 Communications in Mathematics and Statistics 1 Mathematical Sciences 1 Journal of Complex Networks 1 Transactions of A. Razmadze Mathematical Institute 1 Springer Finance
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### Cited in 28 Fields

 75 Operations research, mathematical programming (90-XX) 66 Numerical analysis (65-XX) 32 Statistics (62-XX) 31 Computer science (68-XX) 18 Fluid mechanics (76-XX) 16 Partial differential equations (35-XX) 16 Mechanics of deformable solids (74-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 15 Biology and other natural sciences (92-XX) 9 Geophysics (86-XX) 8 Information and communication theory, circuits (94-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Systems theory; control (93-XX) 5 Optics, electromagnetic theory (78-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Ordinary differential equations (34-XX) 3 Integral equations (45-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of particles and systems (70-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mathematical logic and foundations (03-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX)