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In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities.
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Y. Nesterov, Universal gradient methods for convex optimization problems , Mathematical Programming 152 (2015), pp. 381–404. Available at http://dx.doi.org/10.1007/s10107-014-0790-0
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A. Chernov, P. Dvurechensky, and A. Gasnikov, Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints , in Discrete Optimization and Operations Research: 9th International Conference, DOOR 2016, Vladivostok, Russia, September 19-23, 2016, Proceedings , Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski, and P. Pardalos, eds. Springer International Publishing, 2016, pp. 391–403
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P. Dvurechensky and A. Gasnikov, Stochastic intermediate gradient method for convex problems with stochastic inexact oracle , Journal of Optimization Theory and Applications 171 (2016), pp. 121–145. Available at http://dx.doi.org/10.1007/s10957-016-0999-6
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A.V. Gasnikov and P.E. Dvurechensky, Stochastic intermediate gradient method for convex optimization problems , Doklady Mathematics 93 (2016), pp. 148–151
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A.S. Anikin, A.V. Gasnikov, P.E. Dvurechensky, A.I. Tyurin, and A.V. Chernov, Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints , Computational Mathematics and Mathematical Physics 57 (2017), pp. 1262–1276
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A. Gasnikov, Universal gradient descent , arXiv preprint arXiv:1711.00394 (2017)
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2019
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D. Baimurzina, A. Gasnikov, E. Gasnikova, P. Dvurechensky, E. Ershov, M. Kubentaeva, and A. Lagunovskaya, Universal similar triangulars method for searching equilibriums in traffic flow distribution models , Journal of Computational Mathematics and Mathematical Physics 59 (2019), pp. 21–36
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A.V. Gasnikov, P.E. Dvurechensky, F.S. Stonyakin, and A.A. Titov, An adaptive proximal method for variational inequalities , Computational Mathematics and Mathematical Physics 59 (2019), pp. 836–841. Available at https://doi.org/10.1134/S0965542519050075
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A. Gasnikov and A. Tyurin, Fast gradient descent for convex minimization problems with an oracle producing a ( δ , l ) (\delta,l) -model of function at the requested point , Computational Mathematics and Mathematical Physics 59 (2019), pp. 1085–1097
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S.V. Guminov, Y.E. Nesterov, P.E. Dvurechensky, and A.V. Gasnikov, Accelerated primal-dual gradient descent with linesearch for convex, nonconvex, and nonsmooth optimization problems , Doklady Mathematics 99 (2019), pp. 125–128
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A. Tyurin, Primal-dual fast gradient method with a model , arXiv preprint arXiv:1906.10107 (2019)
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2020
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Y. Malitsky, Golden ratio algorithms for variational inequalities , Mathematical Programming 184 (2020), pp. 383–410. Available at https://doi.org/10.1007/s10107-019-01416-w
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Y. Nesterov and M.I. Florea, Gradient methods with memory , Optimization Methods and Software 0 (2021), pp. 1–18. Available at https://doi.org/10.1080/10556788.2020.1858831
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2020
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M.B. Cohen, A. Sidford, and K. Tian, Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration , in 12th Innovations in Theoretical Computer Science Conference, ITCS 2021, January 6-8, 2021, Virtual Conference , J.R. Lee, ed., LIPIcs Vol. 185. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, pp. 62:1–62:18. Available at https://doi.org/10.4230/LIPIcs.ITCS.2021.62
2021
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