Mathematical modelling of traffic flow, the stochastic analysis and its applications, dynamic systems (ergodic dynamic, concentration of an invariant measure), asymptotical analysis (methods of small parameter), intermediate asymtotic solution of Rieman's type problem for nonlinear parabolic equations (Burgers type, Kolmogorov–Petrovskij–Piskunov-type) and them difference-differential analogues.
Biography
2000–2006 — MIPT student;
с 2006 — MIPT post-graduate student.
Main publications:
A. V. Gasnikov, “Time asymptotic behavior of the solution to a quasilinear parabolic equation”, Computational Mathematics and Mathematical Physics, 46:12 (2006), 2136–2153
A. V. Gasnikov, “On the intermediate asymptotic of the solution to the Cauchy problem for a quasilinear equation of parabolic type with a monotone initial condition”, Journal of Computer and Systems Sciences International, 47:3 (2008), 475–484
A. V. Gasnikov, “Convergence in the form of a solution to the Cauchy problem for a quasilinear parabolic equation with a monotone initial condition to a system of waves”, Computational Mathematics and Mathematical Physics, 48:8 (2008), 1376–1405
F. S. Stonyakin, A. N. Stepanov, A. V. Gasnikov, A. A. Titov, “Mirror descent for constrained optimization problems with large subgradient values of functional constraints”, Computer Research and Modeling, 12:2 (2020), 301–317
2.
D. M. Dvinskikh, A. I. Turin, A. V. Gasnikov, S. S. Omelchenko, “Accelerated and Unaccelerated Stochastic Gradient Descent in Model Generality”, Mat. Zametki, 108:4 (2020), 515–528; Math. Notes, 108:4 (2020), 511–522
2019
3.
E. Vorontsova, A. V. Gasnikov, E. A. Gorbunov, P. E. Dvurechenskii, “Accelerated gradient-free optimization methods with a non-Euclidean proximal operator”, Avtomat. i Telemekh., 2019, 8, 149–168; Autom. Remote Control, 80:8 (2019), 1487–1501
4.
E. A. Vorontsova, A. V. Gasnikov, E. A. Gorbunov, “Accelerated descent along a random direction with non-Euclidean prox-structure”, Avtomat. i Telemekh., 2019, 4, 126–143
5.
E. A. Gorbunov, E. Vorontsova, A. V. Gasnikov, “On the Upper Bound for the Expectation of the Norm of a Vector Uniformly Distributed on the Sphere and the Phenomenon of Concentration of Uniform Measure on the Sphere”, Mat. Zametki, 106:1 (2019), 13–23; Math. Notes, 106:1 (2019), 11–19
6.
E. A. Vorontsova, A. V. Gasnikov, A. S. Ivanova, E. A. Nurminsky, “The Walrasian equilibrium and centralized distributed optimization in terms of modern convex optimization methods on the example of resource allocation problem”, Sib. Zh. Vychisl. Mat., 22:4 (2019), 415–436
7.
A. V. Gasnikov, A. I. Turin, “Быстрый градиентный спуск для задач выпуклой минимизации с оракулом, выдающим $(\delta,L)$-модель функции в запрошенной точке”, Zh. Vychisl. Mat. Mat. Fiz., 59:7 (2019), 1137–1150
8.
A. V. Gasnikov, P. E. Dvurechenskii, F. S. Stonyakin, A. A. Titov, “Адаптивный проксимальный метод для вариационных неравенств”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 889–894
9.
D. R. Baymurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechenskii, E. I. Ershov, M. B. Kubentayeva, A. A. Lagunovskaya, “Универсальный метод поиска равновесий и стохастических равновесий в транспортных сетях”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 21–36
2018
10.
A. S. Bayandina, A. V. Gasnikov, A. A. Lagunovskaya, “Gradient-free two-point methods for solving stochastic nonsmooth convex optimization problems with small non-random noises”, Avtomat. i Telemekh., 2018, 8, 38–49; Autom. Remote Control, 79:8 (2018), 1399–1408
11.
A. V. Gasnikov, E. A. Gorbunov, D. A. Kovalev, A. Mohammed, E. O. Chernousova, “The global rate of convergence for optimal tensor methods in smooth convex optimization”, Computer Research and Modeling, 10:6 (2018), 737–753
12.
A. V. Gasnikov, M. B. Kubentayeva, “Searching stochastic equilibria in transport networks by universal primal-dual gradient method”, Computer Research and Modeling, 10:3 (2018), 335–345
13.
A. V. Gasnikov, D. A. Kovalev, “A hypothesis about the rate of global convergence for optimal methods (Newton's type) in smooth convex optimization”, Computer Research and Modeling, 10:3 (2018), 305–314
14.
P. Dvurechensky, A. Gasnikov, A. Lagunovskaya, “Parallel algorithms and probability of large deviation for stochastic convex optimization problems”, Sib. Zh. Vychisl. Mat., 21:1 (2018), 47–53; Num. Anal. Appl., 11:1 (2018), 33–37
15.
A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Sib. Zh. Vychisl. Mat., 21:1 (2018), 23–45; Num. Anal. Appl., 11:1 (2018), 16–32
16.
A. S. Bayandina, A. V. Gasnikov, E. V. Gasnikova, S. V. Matsievskii, “Primal-dual mirror descent method for constraint stochastic optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018), 1794–1803; Comput. Math. Math. Phys., 58:11 (2018), 1728–1736
17.
A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, “Dual methods for finding equilibriums in mixed models of flow distribution in large transportation networks”, Zh. Vychisl. Mat. Mat. Fiz., 58:9 (2018), 1447–1454; Comput. Math. Math. Phys., 58:9 (2018), 1395–1403
18.
A. V. Gasnikov, Yu. E. Nesterov, “Universal method for stochastic composite optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 58:1 (2018), 52–69; Comput. Math. Math. Phys., 58:1 (2018), 48–64
2017
19.
A. V. Gasnikov, E. A. Krymova, A. A. Lagunovskaya, I. N. Usmanova, F. A. Fedorenko, “Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case”, Avtomat. i Telemekh., 2017, 2, 36–49; Autom. Remote Control, 78:2 (2017), 224–234
20.
A. Gasnikov, E. Gasnikova, P. Dvurechensky, A. Mohammed, E. Chernousova, “About the power law of the PageRank vector distribution. Part 1. Numerical methods for finding the PageRank vector”, Sib. Zh. Vychisl. Mat., 20:4 (2017), 359–378; Num. Anal. Appl., 10:4 (2017), 299–312
21.
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”, Zh. Vychisl. Mat. Mat. Fiz., 57:8 (2017), 1270–1284; Comput. Math. Math. Phys., 57:8 (2017), 1262–1276
2016
22.
A. V. Gasnikov, A. A. Lagunovskaya, I. N. Usmanova, F. A. Fedorenko, “Gradient-free proximal methods with inexact oracle for convex stochastic nonsmooth optimization problems on the simplex”, Avtomat. i Telemekh., 2016, 10, 57–77; Autom. Remote Control, 77:11 (2016), 2018–2034
23.
A. V. Gasnikov, P. E. Dvurechensky, Yu. V. Dorn, Yu. V. Maksimov, “Numerical methods for the problem of traffic flow equilibrium in the Beckmann and the stable dynamic models”, Matem. Mod., 28:10 (2016), 40–64
24.
A. V. Gasnikov, E. V. Gasnikova, M. A. Mendel, K. V. Chepurchenko, “Evolutionary interpretations of entropy model for correspondence matrix calculation”, Matem. Mod., 28:4 (2016), 111–124
25.
A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, A. V. Chernov, “Efficient numerical methods for entropy-linear programming problems”, Zh. Vychisl. Mat. Mat. Fiz., 56:4 (2016), 523–534; Comput. Math. Math. Phys., 56:4 (2016), 514–524
2015
26.
A. V. Gasnikov, “Reduction of searching competetive equillibrium to the minimax problem in application to different network problems”, Matem. Mod., 27:12 (2015), 121–136
27.
A. V. Gasnikov, Yu. E. Nesterov, V. G. Spokoiny, “On the efficiency of a randomized mirror descent algorithm in online optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 582–598; Comput. Math. Math. Phys., 55:4 (2015), 580–596
28.
A. V. Gasnikov, D. Yu. Dmitriev, “On efficient randomized algorithms for finding the PageRank vector”, Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015), 355–371; Comput. Math. Math. Phys., 55:3 (2015), 349–365
2014
29.
A. Gasnikov, Yu. Dorn, Yu. Nesterov, S. Shpirko, “On the three-stage version of stable dynamic model”, Matem. Mod., 26:6 (2014), 34–70
2013
30.
A. V. Gasnikov, E. V. Gasnikova, “On Entropy-Type Functionals Arising in Stochastic Chemical Kinetics Related to the Concentration of the Invariant Measure and Playing the Role of Lyapunov Functions in the Dynamics of Quasiaverages”, Mat. Zametki, 94:6 (2013), 819–827; Math. Notes, 94:6 (2013), 854–861
2012
31.
A. V. Gasnikov, “On the velocity of separation between two successive traveling waves in the asymptotics of the solution to the Cauchy problem for a Burgers-type equation”, Zh. Vychisl. Mat. Mat. Fiz., 52:6 (2012), 1069–1071; Comput. Math. Math. Phys., 52:6 (2012), 937–939
2011
32.
I. I. Morozov, A. V. Gasnikov, V. N. Tarasov, Ya. A. Kholodov, A. S. Kholodov, “Numerical study of traffic flows by the hydrodynamic models”, Computer Research and Modeling, 3:4 (2011), 389–412
2009
33.
A. V. Gasnikov, “Time-asymptotic behaviour of a solution of the Cauchy initial-value problem for a conservation law with non-linear divergent viscosity”, Izv. RAN. Ser. Mat., 73:6 (2009), 39–76; Izv. Math., 73:6 (2009), 1111–1148
2008
34.
A. V. Gasnikov, “Convergence in the form of a solution to the Cauchy problem for a quasilinear parabolic equation with a monotone initial condition to a system of waves”, Zh. Vychisl. Mat. Mat. Fiz., 48:8 (2008), 1458–1487; Comput. Math. Math. Phys., 48:8 (2008), 1376–1405
2006
35.
A. V. Gasnikov, “Time asymptotic behavior of the solution to a quasilinear parabolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:12 (2006), 2235–2253; Comput. Math. Math. Phys., 46:12 (2006), 2136–2153
2018
36.
A. V. Gasnikov, A. I. Lobanov, Ya. A. Kholodov, “Editor's note”, Computer Research and Modeling, 10:3 (2018), 279–283
2012
37.
A. Gasnikov, E. Chernousova, T. Nagapetyan, O. Fed'ko, “Стохастический анализ в задачах”, Mat. Pros., Ser. 3, 16 (2012), 181–213
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