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Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”

Published: 07 December 2011 Publication History

Abstract

This remark describes an improvement and a correction to Algorithm 778. It is shown that the performance of the algorithm can be improved significantly by making a relatively simple modification to the subspace minimization phase. The correction concerns an error caused by the use of routine dpmeps to estimate machine precision.

References

[1]
Byrd, R. H., Lu, P., Nocedal, J., and Zhu, C. 1995. A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16, 5, 1190--1208.
[2]
Fourer, R., Gay, D. M., and Kernighan, B. W. 1993. AMPL: A Modeling Language for Mathematical Programming. Scientific Press. www.ampl.com.
[3]
Gould, N. I. M., Orban, D., and Toint, P. L. 2003a. CUTEr and sifdec: A constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29, 4, 373--394.
[4]
Gould, N. I. M., Orban, D., and Toint, P. L. 2003b. GALAHAD, A library of thread-safe fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Softw. 29, 4, 353--372.
[5]
Lin, C. J. and Moré, J. J. 1999. Newton's method for large bound-constrained optimization problems. SIAM J. Optimiz. 9, 4, 1100--1127.
[6]
Zhu, C., Byrd, R. H., Lu, P., and Nocedal, J. 1997. Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization. ACM Trans. Math. Softw. 23, 4, 550--560.

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        cover image ACM Transactions on Mathematical Software
        ACM Transactions on Mathematical Software  Volume 38, Issue 1
        November 2011
        144 pages
        ISSN:0098-3500
        EISSN:1557-7295
        DOI:10.1145/2049662
        Issue’s Table of Contents
        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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        Publication History

        Published: 07 December 2011
        Accepted: 01 April 2011
        Revised: 01 April 2011
        Received: 01 January 2011
        Published in TOMS Volume 38, Issue 1

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        Author Tags

        1. Nonlinear programming
        2. constrained optimization
        3. infeasibility

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