Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité

Jean Charles Gilbert

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 2, page 251-288
  • ISSN: 0764-583X

How to cite

top

Gilbert, Jean Charles. "Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.2 (1988): 251-288. <http://eudml.org/doc/193530>.

@article{Gilbert1988,
author = {Gilbert, Jean Charles},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {quasi-Newton method; local superlinear convergence; equality-constrained optimization; reduced Hessian methods},
language = {fre},
number = {2},
pages = {251-288},
publisher = {Dunod},
title = {Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité},
url = {http://eudml.org/doc/193530},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Gilbert, Jean Charles
TI - Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 2
SP - 251
EP - 288
LA - fre
KW - quasi-Newton method; local superlinear convergence; equality-constrained optimization; reduced Hessian methods
UR - http://eudml.org/doc/193530
ER -

References

top
  1. L. ARMIJO (1966. Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics 16/1,1-3. Zbl0202.46105MR191071
  2. J BLUM, J. Ch. GILBERT, B. THOORIS (1985). Parametric identification of the plasma current density from the magnetic measurements and the pressure profile, code IDENTC Report of JET contract number JT3/9008. 
  3. J. F. BONNANS, D. GABAY (1984. Une éxtension de la programmation quadratique successive. Lecture Notes in Control and Information Sciences 63, 16-31. A. Bensoussan, J. L Lions (eds). Springer-Verlag. Zbl0559.90081MR876712
  4. C. G. BROYDEN (1969). A new double-rank minimization algorithm. Notices of the American Mathematical Society 16, 670. 
  5. C G. BROYDEN, J. E. DENNIS, J. J. MORE (1973). On the local and superlinear convergence of quasi-Newton methods. Journal of the Institute of Mathematics and its Applications 12, 223-245 Zbl0282.65041MR341853
  6. R. H. BYRD (1985). An example of irregular convergence in some constrained optimization methods that use the projected hessian. Mathematical Programming 32, 232-237. Zbl0576.90079MR793692
  7. R. H. BYRD, R. B. SCHNABEL (1986). Continuity of the null space basis and constrained optimization. Mathematical Programming 35, 32-41. Zbl0598.90072MR842632
  8. T F COLEMAN, A. R. CONN (1982 a). Nonlinear programming via an exact penalty function: asymptotic analysis. Mathematical Programming 24, 123-136. Zbl0501.90078MR674627
  9. T. F. COLEMAN, A. R. CONN (1982 b). Nonlinear programming via an exact penalty function: global analysis. Mathematical Programming 24, 137-161. Zbl0501.90077MR674628
  10. T. F. COLEMAN, A. R. CONN (1984. On the local convergence of a quasi-Newton method for the nonlinear programming problem. SIAM Journal on Numerical Analysis 21/4, 755-769. Zbl0566.65046MR749369
  11. J. E. DENNIS, J. J. MORE (1974) A characterization of superlinear convergence and its application to quasi-Newton methods Mathematics of Computation 28/126, 549-560. Zbl0282.65042MR343581
  12. J. E. DENNIS, J. J. MORE (1977). Quasi-Newton methods, motivation and theory. SIAM Review 19, 46-89. Zbl0356.65041MR445812
  13. R. FLETCHER (1970). A new approach to variable metric algorithms. Journal 13/3, 317-322. Zbl0207.17402
  14. R. FLETCHER (1981). Practical Methods of Optimization Vol. 2 : Constrained Optimization. John Wiley & Sons. Zbl0474.65043MR633058
  15. D. GABAY (1982a). Minimizing a differentiable function over a differential manifold. Journal of Optimization Theory and Applications 37/2, 177-219. Zbl0458.90060MR663521
  16. D. GABAY (1982b). Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization. Mathematical Programming Study 16,18-44. Zbl0477.90065MR650627
  17. R. P. GE, M. J. D. POWELL (1983). The convergence of variable metric matrices in unconstrained optimization Mathematical Programming 27, 123-143. Zbl0532.49015MR718055
  18. J. Ch. GILBERT (1986a). Une méthode à métrique variable réduite en optimisation avec contraintes d'égalité non linéaires Rapport de recherche de l'INRIA RR-482, 78153 Le Chesnay Cedex, France. 
  19. J. Ch. GILBERT (1986b). On the local and global convergence of a reduced quasi-Newton method Rapport de recherche de l'INRIA RR-565, 78153 Le Chesnay Cedex, France (version révisée dans IIASA Workmg Paper WP-87-113). Zbl0676.90061
  20. J. Ch. GILBERT (1986b). Une méthode de quasi-Newton réduite en optimisation sous contraintes avec priorité à la restauration. Lecture Notes in Control and Information Sciences 83, 40-53. A. Bensoussan, J. L. Lions (eds), Sprmger-Verlag. Zbl0599.90112MR870388
  21. J. Ch. GILBERT (-) (en préparation). 
  22. D. GOLDFARB (1970). A family of variable metric methods derived by variational means. Mathematics of Computation 24, 23-26. Zbl0196.18002MR258249
  23. S. P. HAN (1976). Superlinearly convergent variable metric algorithms for general nonlinear programming problems. Mathematical Programming 11, 263-282. Zbl0364.90097MR483440
  24. S. P. HAN (1977). A globally convergent method for nonlinear programming. Journal of Optimization Theory and Applications 22/3, 297-309. Zbl0336.90046MR456497
  25. D. Q. MAYNE, E. POLAK (1982). A superlinearly convergent algorithm for constrained optimization problems. Mathematical Programming Study 16, 45-61. Zbl0477.90071MR650628
  26. H. MUKAI, E. POLAK (1978). On the use of approximations in algorithms for optimization problems with equality and inequality constraints. SIAM Journal on Numerical Analysis 15/4, 674-693. Zbl0392.49017MR497967
  27. J. NOCEDAL, M. L. OVERTON (1985). Projected Hessian updating algorithms for nonlinearly constrained optimization. SIAM Journal on Numerical Analysis 22/5, 821-850. Zbl0593.65043MR799115
  28. M. J. D. POWELL (1971). On the convergence of the variable metric algorithm. Journal of the Institute of Mathematics and its Applications 7, 21-36. Zbl0217.52804MR279977
  29. M. J. D. POWELL (1976). Some global convergence properties of a variable metric algorithm for minimization without exact line searches. Nonlinear Programming, SIAM-AMS Proceedings, Vol. 9, American Mathematical Society, Providence, R.I. Zbl0338.65038MR426428
  30. M. J. D. POWELL(1978). The convergence of variable metric methods for nonlinearly constrained optimization calculations. Nonlinear Programming 3, 27-63. O. L. Mangasarian, R. R. Meyer, S. M. Robinson (eds), Academic Press, New York. Zbl0464.65042MR507858
  31. D. F. SHANNO (1970). Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation 24, 647-656. Zbl0225.65073MR274029
  32. R. B. WILSON (1963). A simplicial algorithm for concave programming. Ph. D. Thesis. Graduate School of Business Administration, Havard Univ., Cambridge, MA. 
  33. Y. YUAN (1985). An only 2-step Q-superlinear convergence example for some algonthms that use reduced Hessian approximations Mathematical Programming 32, 224-231. Zbl0565.90060MR793691

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.