Free Access
RAIRO-Oper. Res.
Volume 31, Number 3, 1997
Page(s) 269 - 294
Published online 10 February 2017
  • 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] [Google Scholar]
  • 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. [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 9. D. M. GAY, Computing optimal locally constrained steps, SIAM J. Sci. Stat. Comput., 1981, 2, pp. 186-197. [MR: 622715] [Zbl: 0467.65027] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 12. D. LUENBERGER, Linear and Nonlinear Programming, Addison Wesley, 1984. [Zbl: 0571.90051] [Google Scholar]
  • 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] [Google Scholar]
  • 14. J. M. MARTÍNEZ, Fixed-point quasi-Newton methods, SIAM Journal on Numerical Analysis, 1992, 5, pp. 1413-1434. [MR: 1182737] [Zbl: 0758.65043] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 18. J. J. MORÉ, Generalizations of the trust-region Problem, Optimization Methods and Software, 1993, 2, pp. 189-209. [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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] [Google Scholar]
  • 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. [Google Scholar]

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