Abstract
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 predessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.
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- BERTSEKAS, D.P. 1982. Projected Newton methods for optimization problems with simple constraints. SIAM J. Contr. Optim. 20, 221-246.]]Google ScholarCross Ref
- BONGARTZ, I., CONN, A. R., GOULD, N., AND TOINT, PH. L. 1995. CUTE: Constrained and unconstrained testing environment. ACM Trans. Math. Softw. 21, 1 (Mar.), 123-160.]] Google ScholarDigital Library
- BUCKLEY, A. 1989. Remark on Algorithm 630. ACM Trans. Math. Softw. 15, 3 (Sept.), 262-274.]] Google ScholarDigital Library
- BUCKLEY, A. AND LENIR, A. 1985. ALGORITHM 630: BBVSCG--a variable-storage algorithm for function minimization. ACM Trans. Math. Softw. 11, 2 (June), 103-119.]] Google ScholarDigital Library
- 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 (Sept.), 1190-1208.]] Google ScholarDigital Library
- BYRD, R. g., NOCEDAL, J., AND SCHNABEL, R. B. 1994. Representations of quasi-Newton matrices and their use in limited memory methods. Math. Program. 63, 2 (Jan. 31), 129-156.]]Google ScholarCross Ref
- CONN, A. R., GOULD, N. I. M., AND TOINT, PH. L. 1988. Testing a class of methods for solving minimization problems with simple bounds on the variables. Math. Comput. 50, 182, 399-430.]]Google ScholarCross Ref
- CONN, A. R., GOULD, N. I. M., AND TOINT, PH. L. 1992. LANCELOT: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A). Springer Series in Computational Mathematics, vol. 17. Springer-Verlag, New York, NY.]] Google ScholarCross Ref
- DENNIS, J. E. AND SCHNABEL, R.B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Inc., Upper Saddle River, NJ.]] Google ScholarDigital Library
- GILBERT, J. C. AND LEMARI~CHAL, C. 1989. Some numerical experiments with variablestorage quasi-Newton algorithms. Math. Program. 45, 3 (Dec.), 407-435.]]Google ScholarCross Ref
- GILL, P. E., MURRAY, W., AND WRIGHT, M.H. 1981. Practical Optimization. Academic Press Ltd., London, UK.]]Google Scholar
- LEVITIN, E. S. AND POLYAK, B.T. 1966. Constrained minimization problems. USSR Comput. Math. Math. Phys. 6, 1-50.]]Google ScholarCross Ref
- LIU, D. C. AND NOCEDAL, J. 1989. On the limited memory BFGS method for large scale optimization. Math. Program. 45, 3 (Dec.), 503-528.]]Google ScholarCross Ref
- MOR}~, J. J. AND THUENTE, D.J. 1994. Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Softw. 20, 3 (Sept.), 286-307.]] Google ScholarDigital Library
- MOR}~, J. J. AND TORALDO, G. 1989. Algorithms for bound constrained quadratic programming problems. Numer. Math. 55, 377-400.]]Google ScholarDigital Library
- SIEGEL, D. 1992. Implementing and modifying Broyden class updates for large scale optimization. Rep. DAMPT 1992/NA12. Cambridge University, Cambridge, MA.]]Google Scholar
- ZHU, C., BYRD, R. H., Lu, P., AND NOCEDAL, J. 1995. L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization. EECS Tech. Rep. NAM12. Northwestern University, Evanston, IL.]]Google Scholar
Index Terms
- Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
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