An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables

SIAM Journal on Optimization

Volumn 8, Issue 2, 1998, Pages 532-560

  Pytlak, R ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Box constraints; Conjugate gradient algorithm; Large scale problems; Projection

Indexed keywords

EID: 0032222090     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623494276518     Document Type: Article

References (29)

1. D. P. BERTSEKAS, On the Goldstein-Levitin-Polyak gradient projection method, IEEE Trans. Automat. Control, 21 (1974), pp. 174-184.
2. D. P. BERTSEKAS, Constrained Optimization and Lagrange Multipliers Methods, Academic Press, New York, 1982.
3. D. P. BERTSEKAS, Projected Newton methods for optimization problems with simple constraints, SIAM J. Control Optim., 20 (1982), pp. 221-245.
4. I. BONGARTZ, A. R. CONN, N. I. M. GOULD, AND Ph. L. TOINT, CUTE: Constrained and Unconstrained Testing Environment, Research report RC 18860, IBM T. J. Watson Research Center, Yorktown Heights, NY, 1994.
5. A. BUCKLEY AND A. LENIR, QN-like variable storage conjugate gradients, Math. Programming, 27 (1983), pp. 155-175.
6. J. V. BURKE AND J. J. MORE, On the identification of active constraints, SIAM J. Numer. Anal., 25 (1988), pp. 1197-1211.
7. J. V. BURKE AND J. J. MORE, Exposing constraints, SIAM J. Optim., 4 (1994), pp. 573-595.
8. R. H. BYRD, P. LU, J. NOCEDAL, AND C. ZHU, A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Comput., 16 (1995), pp. 1190-2108.
9. F. H. CLARKE, Generalized gradients and applications, Trans. Amer. Math. Soc., 205 (1975), pp. 247-262.
10. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM J. Numer. Anal., 28 (1988), pp. 433-460.
11. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, Testing a class of methods for solving minimization problems with simple bounds on the variables, Math. Comp., 50 (1988), pp. 399-430.
12. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, LANCELOT: A Fortran package for large-scale nonlinear optimization (release A), in Springer Series in Computational Mathematics 17, Springer-Verlag, New York, 1992.
13. J. C. DUNN, Gradient projection methods for systems optimization problems, Control Dyn. Syst., 29 (1988), pp. 135-195.
14. R. FLETCHER, Practical Methods of Optimization, John Wiley, Chichester, 1987.
15. R. FLETCHER AND C. M. REEVES, Function minimization by conjugate gradients, Comput. J., 7 (1964), pp. 149-154.
16. J. CH. GILBERT AND C. LEMARÉCHAL, Some numerical experiments with variable-storage Quasi-Newton algorithms, Math. Programming, 45 (1989), pp. 407-436.
17. J. CH. GILBERT AND J. NOCEDAL, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim., 2 (1992), pp. 21-42.
18. A. A. GOLDSTEIN, Convex programming in Hilbert spaces, Bull. Amer. Math. Soc., 70 (1964), pp. 709-710.
19. C. LEMARÉCHAL, An extension of Davidon methods to nondifferentiable problem, in Mathematical Programming Study 3, M. L. Balinski and P. Wolfe, eds., North-Holland, Amsterdam, 1975, pp. 95-109.
20. E. S. LEVITIN AND B. T. POLYAK, Constrained minimization methods, Zh. Vychisl. Mat. i Mat. Fiz., 6 (1965), pp. 787-823 (in Russian).
21. D. C. LIUA AND J. NOCEDAL, On the limited memory BFGS method for large scale optimization problems, Math. Programming, 45 (1989), pp. 503-528.
22. R. MIFFLIN, An algorithm for constrained optimization with semismooth functions, Math. Oper. Res., 2 (1977), pp. 191-207.
23. E. POLAK AND C. RIBIÉRE, Note sur la convergence de methods de directions conjugres, Rev. Francaise Informat. Recherche Operationalle, 16 (1969), pp. 35-43.
24. R. PYTLAK, Numerical experiment with new conjugate direction methods for nondifferentiable optimization, in Proc. 28th IEEE CDC Conference, Tampa, FL, 1989, pp. 2457-2462.
25. R. PYTLAK, On the convergence of conjugate gradient algorithms, IMA J. Numer. Anal., 14 (1994), pp. 443-460.
26. D. F. SHANNO, Conjugate gradient methods with inexact searches, Math. Oper. Res., 3 (1978), pp. 244-256.
27. D. F. SHANNO, On the convergence of a new conjugate gradient algorithm, SIAM J. Numer. Anal., 15 (1978), pp. 1247-1257.
28. P. WOLFE, A method of conjugate subgradients for minimizing nondifferentiable functions, in Math. Programming Stud. 3, M. L. Balinski and P. Wolfe, eds., 1975, pp. 145-173.
29. C. ZHU, R. H. BYRD, P. LU, AND J. NOCEDAL, L-BFGS-B - FORTRAN Subroutines for Large-Scale Bound Constrained Optimization, Research report, Northwestern University, Department of Electrical Engineering and Computer Science, Evanston, IL, 1994.