Geodesic
Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1270-1284

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A strongly convex function of simple structure (for example, separable) is minimized under affine constraints. A dual problem is constructed and solved by applying a fast gradient method. The necessary properties of this method are established relying on which, under rather general conditions, the solution of the primal problem can be recovered with the same accuracy as the dual solution from the sequence generated by this method in the dual space of the problem. Although this approach seems natural, some previously unpublished rather subtle results necessary for its rigorous and complete theoretical substantiation in the required generality are presented. 
@article{ZVMMF_2017_57_8_a3,
     author = {A. S. Anikin and A. V. Gasnikov and P. E. Dvurechensky and A. I. Tyurin and A. V. Chernov},
     title = {Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1270--1284},
     publisher = {mathdoc},
     volume = {57},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a3/}
}
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A. S. Anikin; A. V. Gasnikov; P. E. Dvurechensky; A. I. Tyurin; A. V. Chernov. Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1270-1284. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a3/