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DOI:10.1145/279232.279236 - Corpus ID: 207228122

@article{Zhu1997Algorithm7L, title={Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization}, author={Ciyou Zhu and Richard H. Byrd and Peihuang Lu and Jorge Nocedal}, journal={ACM Trans. Math. Softw.}, year={1997}, volume={23}, pages={550-560}, url={https://api.semanticscholar.org/CorpusID:207228122}}

- C. Zhu, R. Byrd, J. Nocedal
- Published in TOMS 1 December 1997
- Computer Science, Mathematics
- ACM Trans. Math. Softw.

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…

3,056 Citations

167

186

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## Topics

L-BFGS-B (opens in a new tab)Bound-constrained Optimization (opens in a new tab)Hessian Matrix (opens in a new tab)Limited Memory (opens in a new tab)Fortran (opens in a new tab)Nonlinear Optimization Problems (opens in a new tab)

## 3,056 Citations

- J. MoralesJ. Nocedal
- 2011

Mathematics, Computer Science

TOMS

It is shown that the performance of the algorithm can be improved significantly by making a relatively simple modification to the subspace minimization phase.

- 396
- Highly Influenced

- L. LuksanC. MatonohaJ. Vlček
- 2009

Computer Science, Engineering

TOMS

14 basic Fortran subroutines for large- scale unconstrained and box constrained optimization and large-scale systems of nonlinear equations are presented and computational experiments are proposed which demonstrate the efficiency of the proposed algorithms.

- 15
- Highly Influenced

- R. ByrdP. LuJ. NocedalC. Zhu
- 1995

Computer Science, Mathematics

SIAM J. Sci. Comput.

An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the…

- 5,702
- PDF

- Qiuyu WangYing-Jie Che
- 2014

Mathematics, Engineering

Under some appropriate conditions, it is shown that the algorithm converges globally and is promising and competitive with the well-known method—L-BFGS-B.

- W. HenaoM. Overton
- 2014

Mathematics, Computer Science

This thesis investigates a large scale L-BFGS-B optimizer for smooth functions and how it can be modified to optimize non-smooth functions.

- 2
- PDF

- Yunhai XiaoHongchuan Zhang
- 2008

Mathematics, Computer Science

- 6
- PDF

- P. GillW. MurrayM. Saunders
- 2002

Computer Science, Mathematics

SIAM J. Optim.

An SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems is discussed and a reduced-Hessian semidefinite QP solver (SQOPT) is discussed.

- 4,078
- PDF

- J. BrustS. LeyfferC. Petra
- 2020

Mathematics, Computer Science

This article develops the compact representations of two structured Broyden-FletcherGoldfarb-Shanno update formulas, which enable efficient limited memory and initialization strategies.

- 1
- PDF

- Hongchao ZhangW. Hager
- 2006

Computer Science, Mathematics

The adaptive cyclic Barzilai-Borwein (BB) method for unconstrained optimization is extended to bound constrained optimization and performance is compared with SPG2, GENCAN, and L-BFGS-B for bound constrained problems.

- 7
- PDF

- E. BoudinovA. Manevich
- 2007

Computer Science, Engineering

Optim. Methods Softw.

This procedure prevents the set of conjugate vectors from degeneracy and eliminates high sensitivity to computation errors pertinent to methods of CDs, resulting in an efficient algorithm for solving large-scale ill-conditioned minimization problems without preconditioning.

- PDF

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This book, which is concerned with algorithms for solving large-scale non-linear optimization problems, is the only complete source of documentation for the software package Lancelot and will mainly…

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SIAM J. Sci. Comput.

An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the…

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The numerical tests indicate that the L-BFGS method is faster than the method of Buckley and LeNir, and is better able to use additional storage to accelerate convergence, and the convergence properties are studied to prove global convergence on uniformly convex problems.

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An update formula which generates matrices using information from the last m iterations, where m is any number supplied by the user, and the BFGS method is considered to be the most efficient.

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SummaryWe present an algorithm which combines standard active set strategies with the gradient projection method for the solution of quadratic programming problems subject to bounds. We show, in…

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The algorithm BBVSCG is such that one can expect a more efficient and rapid convergence to the minimum and is based on an earlier algorithm, namely, CONMIN, but offers a fundamental facility which was not available in CONMIN.

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A trust region version of Newton's method for bound-constrained problems that holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints.

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1981 20th IEEE Conference on Decision and Control…

It is shown that Dk can be calculated simply on the basis of second derivatives of f so that the resulting Newton-like algorithm has a typically superlinear rate of convergence.

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It is found appropriate to use a diagonal matrix, generated by an update of the identity matrix, so as to fit the Rayleigh ellipsoid of the local Hessian in the direction of the change in the gradient.

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This work derives compact representations of BFGS and symmetric rank-one matrices for optimization and presents a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.

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