Newton's method for large bound-constrained optimization problems

SIAM Journal on Optimization

Volumn 9, Issue 4, 1999, Pages 1100-1127

  Lin, Chih Jen ^a   Moré, Jorge J ^b  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

Bound constrained optimization; Preconditioned conjugate gradients; Projected gradients; Strict complementarity

Indexed keywords

EID: 0033436056     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623498345075     Document Type: Article

References (37)

1. B. M. AVERICK, R. G. CARTER, J. J. MORÉ, AND G.-L. XUE, The MINPACK-2 test problem collection, Preprint MCS-P153-0694, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1992.
2. D. P. BERTSEKAS, Projected Newton methods for optimization problems with simple constraints, SIAM J. Control Optim., 20 (1982), pp. 221-246.
3. I. BONGARTZ, A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, CUTE: Constrained and unconstrained testing environment, ACM Trans. Math. Software, 21 (1995), pp. 123-160.
4. A. BOUARICHA, J. J. MORÉ, AND Z. WU, Preconditioning Newton's Method, Preprint ANL/MCS-P715-0598, Argonne National Laboratory, Argonne, IL, 1998.
5. J. V. BURKE AND J. J. MORÉ, On the identification of active constraints, SIAM J. Numer. Anal., 25 (1988), pp. 1197-1211.
6. J. V. BURKE AND J. J. MORÉ, Exposing constraints, SIAM J. Optim., 4 (1994), pp. 573-595.
7. J. V. BURKE, J. J. MORÉ, AND G. TORALDO, Convergence properties of trust region methods for linear and convex constraints, Math. Programming, 47 (1990), pp. 305-336.
8. P. H. CALAMAI AND J. J. MORÉ, Projected gradient methods for linearly constrained problems, Math. Programming, 39 (1987), pp. 93-116.
9. T. F. COLEMAN AND Y. LI, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim., 6 (1996), pp. 418-445.
10. T. F. COLEMAN AND Y. LI, A Trust Region and Affine Scaling Interior Point Method for Nonconvex Minimization with Linear Inequality Constraints, Technical Report TR97-1642, Cornell University, Ithaca, NY, 1997.
11. T. F. COLEMAN AND Y. LI, Combining trust region and affine scaling for linearly constrained nonconvex minimization, in Advances in Nonlinear Programming, Y. Yuan, ed., Kluwer Academic Publishers, Norwell, MA, 1998, pp. 219-250.
12. A. R. CONN, N. I. M. GOULD, A. SARTENAER, AND P. L. TOINT, Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints, SIAM J. Optim., 3 (1993), pp. 164-221.
13. 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., 25 (1988), pp. 433-460; correction in SIAM J. Numer. Anal., 26 (1989), pp. 764-767.
14. 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., 25 (1988), pp. 433-460; correction in SIAM J. Numer. Anal., 26 (1989), pp. 764-767.
15. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, LANCELOT, Springer Ser. Comput. Math., Springer, New York, 1992.
16. A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization, Math. Programming, 73 (1996) pp. 73-110.
17. J. E. DENNIS AND L. N. VICENTE, Trust-region interior-point algorithms for minimization problems with simple bounds, in Applied Mathematics and Parallel Computing, Festschrift for Klaus Ritter, H. Fisher, B. Riedmüller, and S. Schäffler, eds., Physica, Heidelberg, 1996, pp. 97-107.
18. J. C. DUNN, On the convergence of projected gradient processes to singular critical points, J. Optim. Theory Appl., 55 (1987), pp. 203-216.
19. F. FACCHINEI, J. JÚDICE, AND J. SOARES, An active set Newton's algorithm for large-scale nonlinear programs with box constraints, SIAM J. Optim., 8 (1998), pp. 158-186.
20. F. FACCHINEI AND S. LUCIDI, A Class of Methods for Optimization Problems with Simple Bounds, Technical Report R.336, IASI-CNR, Rome, Italy, 1992.
21. A. FORSGREN AND W. MURRAY, Newton methods for large-scale linear inequality-constrained minimization, SIAM J. Optim., 7 (1997), pp. 162-176.
22. A. FRIEDLANDER, J. M. MARTÍNEZ, AND S. A. SANTOS, A new trust region algorithm for bound constrained minimization, Appl. Math. Optim., 30 (1994), pp. 235-266.
23. E. M. GAFNI AND D. P. BERTSEKAS, Two-metric projection methods for constrained optimization, SIAM J. Control Optim., 22 (1984), pp. 936-964.
24. D. M. GAY, A trust region approach to linearly constrained optimization, in Numerical Analysis, D. F. Griffiths, ed., Lecture Notes in Math. 1066, Springer, New York, 1984, pp. 72-105.
25. M. HEINKENSCHLOSS, M. ULBRICH, AND S. ULBRICH, Superlinear and Quadratic Convergence of Affine-Scaling Interior-Point Newton Methods for Problems with Simple Bounds without Strict Complementarity Assumption, Technical Report TR97-30, Rice University, Houston, TX, 1997; Math. Programming, to appear.
26. M. LESCRENIER, Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold, SIAM J. Numer. Anal., 28 (1991), pp. 476-495.
27. C.-J. LIN AND J. J. MORÉ, Incomplete Cholesky factorizations with limited memory, SIAM J. Sci. Comput., 21 (1999), pp. 24-45.
28. J. J. MORÉ, Trust regions and projected gradients, in Systems Modelling and Optimization, M. Iri and K. Yajima, eds., Lecture Notes in Control and Inform. Sci. 113, Springer, New York, 1988, pp. 1-13.
29. J. J. MORÉ, Global methods for nonlinear complementarity problems, Math. Oper. Res., 21 (1996), pp. 589-614.
30. J. J. MORÉ AND D. C. SORENSEN, Computing a trust region step, SIAM J. Sci. Statist. Comput., 4 (1983), pp. 553-572.
31. J. J. MORÉ AND G. TORALDO, On the solution of large quadratic programming problems with bound constraints, SIAM J. Optim., 1 (1991), pp. 93-113.
32. N. MUNKSGAARD, Solving sparse symmetric sets of linear equations by preconditioned conjugate gradients, ACM Trans. Math. Software, 6 (1980), pp. 206-219.
33. S. M. ROBINSON, Strongly regular generalized equations, Math. Oper. Res., 5 (1980), pp. 43-62.
34. A. SCHWARTZ AND E. POLAK, Family of projected descent methods for optimization problems with simple bounds, J. Optim. Theory Appl., 92 (1997), pp. 1-31.
35. T. STEIHAUG, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 20 (1983), pp. 626-637.
36. PH. L. TOINT, Global convergence of a class of trust region methods for nonconvex minimization in Hubert space, IMA J. Numer. Anal., 8 (1988), pp. 231-252.
37. C. ZHU, R. H. BYRD, P. LU, AND J. NOCEDAL, L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Softw., 23 (1997), pp. 550-560.