New convergence results on an algorithm for norm constrained regularization and related problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 31 (1997) no. 3, pp. 269-294.
@article{RO_1997__31_3_269_0,
author = {Mart{\'\i}nez, Jos\'e Mario and Santos, Sandra Augusta},
title = {New convergence results on an algorithm for norm constrained regularization and related problems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {269--294},
publisher = {EDP-Sciences},
volume = {31},
number = {3},
year = {1997},
zbl = {0887.90160},
mrnumber = {1462321},
language = {en},
url = {http://archive.numdam.org/item/RO_1997__31_3_269_0/}
}
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AU  - Santos, Sandra Augusta
TI  - New convergence results on an algorithm for norm constrained regularization and related problems
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 1997
DA  - 1997///
SP  - 269
EP  - 294
VL  - 31
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/RO_1997__31_3_269_0/
UR  - https://zbmath.org/?q=an%3A0887.90160
UR  - https://www.ams.org/mathscinet-getitem?mr=1462321
LA  - en
ID  - RO_1997__31_3_269_0
ER  - 
Martínez, José Mario; Santos, Sandra Augusta. New convergence results on an algorithm for norm constrained regularization and related problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 31 (1997) no. 3, pp. 269-294. http://archive.numdam.org/item/RO_1997__31_3_269_0/

1. J. Abadie and J. Carpentier, Generalization of the Wolfe reduced-gradient method to the case of nonlinear constraints, in Optimization, R. Fletcher (Ed.), Academic Press, London, 1969. | MR 284206 | Zbl 0254.90049

2. S. D. B. Bitar and A. Friedlander, On the identification properties of a trust-region algorithm on domains given by nonlinear inequalities, Relatório Técnico, Instituto de Matemática, Universidade Estadual de Campinas, Brazil 1995.

3. P. T. Boggs, J. W. Tolle and P. Wang, On the local convergence of quasi-Newton methods for constrained optimization, SIAM Journal on Control and Optimization, 1982, 20, pp. 161-171. | MR 646946 | Zbl 0494.65036

4. M. R. Celis, J. E. Dennis and R. A. Tapia, A trust region strategy for nonlinear equality constrained optimization, in Numerical Optimization, (P. T. Boggs, R. Byrd and R. Schnabel, eds.), SIAM, Philadelphia, 1984, pp. 71-82. | MR 802084 | Zbl 0566.65048

5. 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 Journal on Numerical Analysis, 1988, 25, pp. 433-460. See also SIAM Journal on Numerical Analysis, 1989, 26, pp. 764-767. | MR 933734 | Zbl 0643.65031

6. M. M. El-Alem, A global convergence theory for the Celis-Dennis-Tapia trust region algorithm for constrained optimization, SIAM Journal on Numerical Analysis, 1991, 28, pp. 266-290. | MR 1083336 | Zbl 0725.65061

7. R. Fletcher, Practical Methods of Optimization, (2nd edition), John Wiley and Sons, Chichester, New York, Brisbane, Toronto and Singapore, 1987. | MR 955799 | Zbl 0474.65043

8. A. Friedlander, J. M. Martínez and S. A. Santos, A new algorithm for bound constrained minimization, Journal of Applied Mathematics and Optimization, 1994, 30, pp. 235-266. | MR 1288591 | Zbl 0821.90101

9. D. M. Gay, Computing optimal locally constrained steps, SIAM J. Sci. Stat. Comput., 1981, 2, pp. 186-197. | MR 622715 | Zbl 0467.65027

10. M. Heinkenschloss, Mesh independence for nonlinear least squares problems with norm constraints, SIAM Journal on Optimization, 1993, 3, pp. 81-117. | MR 1202003 | Zbl 0771.65030

11. L. S. Lasdon, Reduced gradient methods, in Nonlinear Optimization 1981, 1982, edited by M. J. D. Powell, Academic Press, New York, pp. 235-242. | MR 775351 | Zbl 0589.90067

12. D. Luenberger, Linear and Nonlinear Programming, Addison Wesley, 1984. | Zbl 0571.90051

13. D. Lyle and M. Szularz, Local minima of the trust-region problem, Journal of Optimization Theory an Applications, 1994, 80, pp. 117-134. | MR 1256140 | Zbl 0797.90096

14. J. M. Martínez, Fixed-point quasi-Newton methods, SIAM Journal on Numerical Analysis, 1992, 5, pp. 1413-1434. | MR 1182737 | Zbl 0758.65043

15. J. M. Martínez, Local minimizers of quadratic functions on Euclidean balls and spheres, SIAM Journal on Optimization, 1994, 4, pp. 159-176. | MR 1260413 | Zbl 0801.65057

16. J. M. Martínez and S. A. Santos, A trust-region strategy for minimization on arbitrary domains, Mathematical Programming, 1995, 68, pp. 267-301. | MR 1319524 | Zbl 0835.90092

17. J. J. Moré, Recent developments in algorithms and software for trust region methods, in Mathematical Programming Bonn 1982. The State of Art, A. Bachem, M. Grötschel and B. Korte, eds., Springer-Verlag, 1983. | MR 717404 | Zbl 0546.90077

18. J. J. Moré, Generalizations of the trust-region Problem, Optimization Methods and Software, 1993, 2, pp. 189-209.

19. J. J. Moré and D. C. Sorensen, Computing a trust region step, SIAM Journal on Scientific and Statistical Computing, 1983, 4, pp. 553-572. | MR 723110 | Zbl 0551.65042

20. M. J. D. Powell and Y. Yuan, A trust region algorithm for equality constrained optimization, Mathematical Programming, 1991, 49, pp. 189-211. | MR 1087453 | Zbl 0816.90121

21. R. J. Stern and H. Wolkowicz, Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations, Technical Report SOR 93-1, School of Engineering and Applied Science, Department of Civil Engineering and Operations Research, Princeton University, 1993. | MR 1282693 | Zbl 0846.49017

22. D. C. Sorensen, Newton's method with a model trust region modification, SIAM Journal on Numerical Analysis, 1982, 19, pp. 409-426. | MR 650060 | Zbl 0483.65039

23. A. Tikhonov and V. Arsenin, Solutions of ill-posed problems, John Wiley and Sons, New York, Toronto, London, 1977. | MR 455365 | Zbl 0354.65028

24. C. R. Vogel, A constrained least-squares regularization method for nonlinear ill-posed problems, SIAM Journal on Control and Optimization, 1990, 28, pp. 34-49. | MR 1035971 | Zbl 0696.65096

25. H. Wolkowicz, On the resolution of the trust region problem, Communication at the NATO-ASI Meeting on Continuons Optimization, II Ciocco, Italy, September 1993, 1993.