Geodesic
About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set
Journal of convex analysis, Tome 24 (2017) no. 2, pp. 493-5
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We consider the gradient projection algorithm for a strongly convex function with the Lipschitz continuous gradient and a proximally smooth (nonconvex in general) set in a real Hilbert space. We prove that the problem of minimization of such function on a proximally smooth set has unique solution if the constant of proximal smoothness of the set is sufficiently large. The considered algorithm converges with the rate of geometric progression.
Classification : 46C05, 52A07, 49J52, 46N10, 90C26, 26B25
Mots-clés : Hilbert space, strongly convex set of radius r, proximally smooth set with constant R, Lipschitz continuous gradient, gradient projection algorithm, continuous optimization 
@article{JCA_2017_24_2_JCA_2017_24_2_a7,
     author = {M. V. Balashov},
     title = {About the {Gradient} {Projection} {Algorithm} for a {Strongly} {Convex} {Function} and a {Proximally} {Smooth} {Set}},
     journal = {Journal of convex analysis},
     pages = {493--5},
     year = {2017},
     volume = {24},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a7/}
}
TY  - JOUR
AU  - M. V. Balashov
TI  - About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set
JO  - Journal of convex analysis
PY  - 2017
SP  - 493
EP  - 5
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a7/
ID  - JCA_2017_24_2_JCA_2017_24_2_a7
ER  - 
%0 Journal Article
%A M. V. Balashov
%T About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set
%J Journal of convex analysis
%D 2017
%P 493-5
%V 24
%N 2
%U http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a7/
%F JCA_2017_24_2_JCA_2017_24_2_a7
M. V. Balashov. About the Gradient Projection Algorithm for a Strongly Convex Function and a Proximally Smooth Set. Journal of convex analysis, Tome 24 (2017) no. 2, pp. 493-5. http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a7/