Geodesic
The general theory of relaxation processes for convex functionals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 25 (1970) no. 1, pp. 57-117

Voir la notice de l'article provenant de la source Math-Net.Ru

This article sets out a theory of the convergence of minimization processes convex functionals that reduce the value of the functional at each step. A geometrical language, independent of the algorithmic structure, is used to describe the processes: the language of relaxation angles and factors. Convergence conditions are derived and the rate of convergence and stability of the process are studied in this terminology. Translation from the language of concrete algorithms to the geometrical terminology is not difficult, and thanks to this the theory has a wide area of applications: gradient and operator-gradient processes, processes of Newtonian type, coordinate relaxation, Jacobi processes and relaxation for the Rayleigh functional. 
@article{RM_1970_25_1_a1,
     author = {Yu. I. Lyubich and G. D. Maistrovskii},
     title = {The general theory of relaxation processes for convex functionals},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {57--117},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1970_25_1_a1/}
}
TY  - JOUR
AU  - Yu. I. Lyubich
AU  - G. D. Maistrovskii
TI  - The general theory of relaxation processes for convex functionals
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 1970
SP  - 57
EP  - 117
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_1970_25_1_a1/
LA  - en
ID  - RM_1970_25_1_a1
ER  - 
%0 Journal Article
%A Yu. I. Lyubich
%A G. D. Maistrovskii
%T The general theory of relaxation processes for convex functionals
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 1970
%P 57-117
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_1970_25_1_a1/
%G en
%F RM_1970_25_1_a1
Yu. I. Lyubich; G. D. Maistrovskii. The general theory of relaxation processes for convex functionals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 25 (1970) no. 1, pp. 57-117. http://geodesic.mathdoc.fr/item/RM_1970_25_1_a1/