Geodesic
An adaptive analog of Nesterov's method for variational inequalities with a strongly monotone operator
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 2, pp. 201-211

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An adaptive analog of the Nesterov method for variational inequalities with a strongly monotone operator is proposed. The main idea of the method proposed is the adaptive choice of constants in maximized concave functional at each iteration. In this case there is no need in specifying an exact value of this constant, because the method proposed makes possible to find a suitable constant at each iteration. Some estimates for the parameters determining the quality of the solution of the variational inequality depending on the number of iterations have been obtained. 
@article{SJVM_2019_22_2_a6,
     author = {F. S. Stonyakin},
     title = {An adaptive analog of {Nesterov's} method for variational inequalities with a strongly monotone operator},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {201--211},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_2_a6/}
}
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F. S. Stonyakin. An adaptive analog of Nesterov's method for variational inequalities with a strongly monotone operator. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 2, pp. 201-211. http://geodesic.mathdoc.fr/item/SJVM_2019_22_2_a6/