Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité
- Volume: 22, Issue: 2, page 251-288
- ISSN: 0764-583X
Access Full Article
topHow to cite
topGilbert, 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- L. ARMIJO (1966. Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics 16/1,1-3. Zbl0202.46105MR191071
- 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.
- 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
- C. G. BROYDEN (1969). A new double-rank minimization algorithm. Notices of the American Mathematical Society 16, 670.
- 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
- 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
- R. H. BYRD, R. B. SCHNABEL (1986). Continuity of the null space basis and constrained optimization. Mathematical Programming 35, 32-41. Zbl0598.90072MR842632
- T F COLEMAN, A. R. CONN (1982 a). Nonlinear programming via an exact penalty function: asymptotic analysis. Mathematical Programming 24, 123-136. Zbl0501.90078MR674627
- T. F. COLEMAN, A. R. CONN (1982 b). Nonlinear programming via an exact penalty function: global analysis. Mathematical Programming 24, 137-161. Zbl0501.90077MR674628
- 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
- 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
- J. E. DENNIS, J. J. MORE (1977). Quasi-Newton methods, motivation and theory. SIAM Review 19, 46-89. Zbl0356.65041MR445812
- R. FLETCHER (1970). A new approach to variable metric algorithms. Journal 13/3, 317-322. Zbl0207.17402
- R. FLETCHER (1981). Practical Methods of Optimization Vol. 2 : Constrained Optimization. John Wiley & Sons. Zbl0474.65043MR633058
- D. GABAY (1982a). Minimizing a differentiable function over a differential manifold. Journal of Optimization Theory and Applications 37/2, 177-219. Zbl0458.90060MR663521
- D. GABAY (1982b). Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization. Mathematical Programming Study 16,18-44. Zbl0477.90065MR650627
- R. P. GE, M. J. D. POWELL (1983). The convergence of variable metric matrices in unconstrained optimization Mathematical Programming 27, 123-143. Zbl0532.49015MR718055
- 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.
- 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
- 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
- J. Ch. GILBERT (-) (en préparation).
- D. GOLDFARB (1970). A family of variable metric methods derived by variational means. Mathematics of Computation 24, 23-26. Zbl0196.18002MR258249
- S. P. HAN (1976). Superlinearly convergent variable metric algorithms for general nonlinear programming problems. Mathematical Programming 11, 263-282. Zbl0364.90097MR483440
- S. P. HAN (1977). A globally convergent method for nonlinear programming. Journal of Optimization Theory and Applications 22/3, 297-309. Zbl0336.90046MR456497
- D. Q. MAYNE, E. POLAK (1982). A superlinearly convergent algorithm for constrained optimization problems. Mathematical Programming Study 16, 45-61. Zbl0477.90071MR650628
- 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
- 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
- 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
- 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
- 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
- D. F. SHANNO (1970). Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation 24, 647-656. Zbl0225.65073MR274029
- R. B. WILSON (1963). A simplicial algorithm for concave programming. Ph. D. Thesis. Graduate School of Business Administration, Havard Univ., Cambridge, MA.
- 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 ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.