Practical active-set Euclidian trust-region method with spectral projected gradients for bound-constrained minimization

Optimization

Volumn 54, Issue 3, 2005, Pages 305-325

  Andretta, Marina ^a   Birgin, Ernesto G ^a   Martínez, José Mario ^b  

^a Institute of Mathematics and Statistics   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Bound constrained optimization; Projected gradient; Spectral gradient; Trust regions

Indexed keywords

EID: 20744447368     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331930500100270     Document Type: Article

References (22)

1. Birgin, E.G. and Martínez, J.M., 2001, A box constrained optimization algorithm with negative curvature directions and spectral projected gradients. Computing Supplement, 15, 49-60.
2. Birgin, E.G. and Martínez, J.M., 2002, Large-scale active-set box- constrained optimization method with spectral projected gradients. Computational Optimization and Applications, 23, 101-125.
3. Burdakov, O., Martínez, J.M. and Pilotta, E.A., 2002, A limited memory multipoint secant method for bound constrained optimization. Annals of Operations Research, 117, 51-70.
4. Zhang, J. and Xu, C., 1999, A class of indefinite dogleg path methods for unconstrained minimization. SIAM Journal on Optimization, 9, 646-667.
5. Moré, J.J., 1983, Recent developments in algorithms and software for trust region methods. In: A. Bachem, M. Grötschel and B. Korte (Eds), Mathematical Programming Bonn 1982 - The State of Art (Berlin: Springer-Verlag).
6. Sorensen, D.C., 1982, Newton's method with a model trust region modification. SIAM Journal on Numerical Analysis, 19, 409-426.
7. Martínez, J.M. and Santos, S.A., 1995, A trust region strategy for minimization on arbitrary domains. Mathematical Programming, 68, 267-302.
8. Martínez, J.M. and Santos, S.A., 1997, Convergence results on an algorithm for norm constrained regularization and related problems. RAIRO Operations Research, 31, 269- 294.
9. Conn, A.R., Gould, N.I.M. and Toint, Ph.L., 1991, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM Journal on Numerical Analysis, 28, 545-572.
10. Friedlander, A., Martínez, J.M. and Santos, S.A., 1994, A new trust region algorithm for bound constrained minimization. Applied Mathematics and Optimization, 30, 235-266.
11. Gay, D.M., 1981, Computing optimal locally constrained steps. SIAM Journal on Scientific and Statistical Computing, 2, 186-197.
12. Moré, J.J. and Sorensen, D.C., 1983, Computing a trust region step. SIAM Journal on Scientific and Statistical Computing, 4, 553-572.
13. Coleman, T.F. and Li, Y., 1996, An interior trust-region approach for nonlinear minimization subject to bounds. SIAM Journal on Optimization, 6, 418-445.
14. Dennis, J.E. and Vicente, L.N., 1996, Trust-region interior-point algorithms for minimization with simple bounds. In: K. Ritter, H. Fisher, B. Riedmuller and S. Schaffer (Eds), Applied Mathematics and Parallel Computing (Heidelberg: Physica), pp. 97-107.
15. Birgin, E.G., Martínez, J.M. and Raydan, M., 2000, Nonmonotone spectral projected gradient methods on convex sets. SIAM Journal on Optimization, 10, 1196-1211.
16. Birgin, E.G., Martínez, J.M. and Raydan, M., 2001, Algorithm 813: SPG - Software for convex-constrained optimization. ACM Transactions on Mathematical Software, 27, 340-349.
17. Birgin, E.G., Martínez, J.M. and Raydan, M., 2003, Inexact spectral projected gradient methods on convex sets. IMA Journal on Numerical Analysis, 23, 539-559.
18. Friedlander, A. and Martínez, J.M., 1994, On the maximization of a concave quadratic function with box constraints. SIAM Journal on Optimization, 4, 177-192.
19. Fletcher, R., 1987, Practical Methods of Optimization (Chichester, New York, Brisbane, Toronto, Singapore: John Wiley & Sons).
20. Bongartz, I., Conn, A.R., Gould, N.I.M. and Toint, Ph. L., 1995, CUTE: constrained and unconstrained testing environment. ACM Transactions on Mathematical Software, 21, 123-160.
21. Rojas, M., Santos, S.A. and Sorensen, D.C., 2000, A new matrix-free algorithm for the large-scale trust-region subproblem. SIAM Journal on Optimization, 11, 611-646.
22. Dolan, E.D. and Moré, J.J., 2002, Benchmarking optimization software with performance profiles. Mathematical Programming, 91, 201-213.