Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité
ESAIM: Modélisation mathématique et analyse numérique, Tome 22 (1988) no. 2, pp. 251-288. 
@article{M2AN_1988__22_2_251_0,
     author = {Gilbert, Jean Charles},
     title = {Mise \`a jour de la m\'etrique dans les m\'ethodes de {quasi-Newton} r\'eduites en optimisation avec contraintes d'\'egalit\'e},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {251--288},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {22},
     number = {2},
     year = {1988},
     mrnumber = {945125},
     zbl = {0657.65087},
     language = {fr},
     url = {http://archive.numdam.org/item/M2AN_1988__22_2_251_0/}
}
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Gilbert, Jean Charles. Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité. ESAIM: Modélisation mathématique et analyse numérique, Tome 22 (1988) no. 2, pp. 251-288. http://archive.numdam.org/item/M2AN_1988__22_2_251_0/

L. Armijo (1966. Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics 16/1,1-3. | MR | Zbl

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. | MR | Zbl

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 | MR | Zbl

R. H. Byrd (1985). An example of irregular convergence in some constrained optimization methods that use the projected hessian. Mathematical Programming 32, 232-237. | MR | Zbl

R. H. Byrd, R. B. Schnabel (1986). Continuity of the null space basis and constrained optimization. Mathematical Programming 35, 32-41. | MR | Zbl

T F Coleman, A. R. Conn (1982 a). Nonlinear programming via an exact penalty function: asymptotic analysis. Mathematical Programming 24, 123-136. | MR | Zbl

T. F. Coleman, A. R. Conn (1982 b). Nonlinear programming via an exact penalty function: global analysis. Mathematical Programming 24, 137-161. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

J. E. Dennis, J. J. More (1977). Quasi-Newton methods, motivation and theory. SIAM Review 19, 46-89. | MR | Zbl

R. Fletcher (1970). A new approach to variable metric algorithms. Journal 13/3, 317-322. | Zbl

R. Fletcher (1981). Practical Methods of Optimization Vol. 2 : Constrained Optimization. John Wiley & Sons. | MR | Zbl

D. Gabay (1982a). Minimizing a differentiable function over a differential manifold. Journal of Optimization Theory and Applications 37/2, 177-219. | MR | Zbl

D. Gabay (1982b). Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization. Mathematical Programming Study 16,18-44. | MR | Zbl

R. P. Ge, M. J. D. Powell (1983). The convergence of variable metric matrices in unconstrained optimization Mathematical Programming 27, 123-143. | MR | Zbl

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). | Zbl

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. | MR | Zbl

J. Ch. Gilbert (-) (en préparation).

D. Goldfarb (1970). A family of variable metric methods derived by variational means. Mathematics of Computation 24, 23-26. | MR | Zbl

S. P. Han (1976). Superlinearly convergent variable metric algorithms for general nonlinear programming problems. Mathematical Programming 11, 263-282. | MR | Zbl

S. P. Han (1977). A globally convergent method for nonlinear programming. Journal of Optimization Theory and Applications 22/3, 297-309. | MR | Zbl

D. Q. Mayne, E. Polak (1982). A superlinearly convergent algorithm for constrained optimization problems. Mathematical Programming Study 16, 45-61. | MR | Zbl

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. | MR | Zbl

J. Nocedal, M. L. Overton (1985). Projected Hessian updating algorithms for nonlinearly constrained optimization. SIAM Journal on Numerical Analysis 22/5, 821-850. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

D. F. Shanno (1970). Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation 24, 647-656. | MR | Zbl

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. | MR | Zbl