New convergence results on an algorithm for norm constrained regularization and related problems
José Mario Martínez; Sandra Augusta Santos
RAIRO - Operations Research - Recherche Opérationnelle (1997)
- Volume: 31, Issue: 3, page 269-294
- ISSN: 0399-0559
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topMartínez, José Mario, and Santos, Sandra Augusta. "New convergence results on an algorithm for norm constrained regularization and related problems." RAIRO - Operations Research - Recherche Opérationnelle 31.3 (1997): 269-294. <http://eudml.org/doc/105151>.
@article{Martínez1997,
author = {Martínez, José Mario, Santos, Sandra Augusta},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {fixed-point quasi-Newton methods; constrained least-squares regularization; nonlinear ill-posed problems; trust-region},
language = {eng},
number = {3},
pages = {269-294},
publisher = {EDP-Sciences},
title = {New convergence results on an algorithm for norm constrained regularization and related problems},
url = {http://eudml.org/doc/105151},
volume = {31},
year = {1997},
}
TY - JOUR
AU - Martínez, José Mario
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
PB - EDP-Sciences
VL - 31
IS - 3
SP - 269
EP - 294
LA - eng
KW - fixed-point quasi-Newton methods; constrained least-squares regularization; nonlinear ill-posed problems; trust-region
UR - http://eudml.org/doc/105151
ER -
References
top- 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. Zbl0254.90049MR284206
- 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. Zbl0494.65036MR646946
- 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. Zbl0566.65048MR802084
- 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. Zbl0643.65031MR933734
- 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. Zbl0725.65061MR1083336
- 7. R. FLETCHER, Practical Methods of Optimization, (2nd edition), John Wiley and Sons, Chichester, New York, Brisbane, Toronto and Singapore, 1987. Zbl0474.65043MR955799
- 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. Zbl0821.90101MR1288591
- 9. D. M. GAY, Computing optimal locally constrained steps, SIAM J. Sci. Stat. Comput., 1981, 2, pp. 186-197. Zbl0467.65027MR622715
- 10. M. HEINKENSCHLOSS, Mesh independence for nonlinear least squares problems with norm constraints, SIAM Journal on Optimization, 1993, 3, pp. 81-117. Zbl0771.65030MR1202003
- 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. Zbl0589.90067MR775351
- 12. D. LUENBERGER, Linear and Nonlinear Programming, Addison Wesley, 1984. Zbl0571.90051
- 13. D. LYLE and M. SZULARZ, Local minima of the trust-region problem, Journal of Optimization Theory an Applications, 1994, 80, pp. 117-134. Zbl0797.90096MR1256140
- 14. J. M. MARTÍNEZ, Fixed-point quasi-Newton methods, SIAM Journal on Numerical Analysis, 1992, 5, pp. 1413-1434. Zbl0758.65043MR1182737
- 15. J. M. MARTÍNEZ, Local minimizers of quadratic functions on Euclidean balls and spheres, SIAM Journal on Optimization, 1994, 4, pp. 159-176. Zbl0801.65057MR1260413
- 16. J. M. MARTÍNEZ and S. A. SANTOS, A trust-region strategy for minimization on arbitrary domains, Mathematical Programming, 1995, 68, pp. 267-301. Zbl0835.90092MR1319524
- 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. Zbl0546.90077MR717404
- 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. Zbl0551.65042MR723110
- 20. M. J. D. POWELL and Y. YUAN, A trust region algorithm for equality constrained optimization, Mathematical Programming, 1991, 49, pp. 189-211. Zbl0816.90121MR1087453
- 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. Zbl0846.49017MR1282693
- 22. D. C. SORENSEN, Newton's method with a model trust region modification, SIAM Journal on Numerical Analysis, 1982, 19, pp. 409-426. Zbl0483.65039MR650060
- 23. A. TIKHONOV and V. ARSENIN, Solutions of ill-posed problems, John Wiley and Sons, New York, Toronto, London, 1977. Zbl0354.65028MR455365
- 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. Zbl0696.65096MR1035971
- 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.
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