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
A. Sadchikov, S. Chezhegov, A. N. Beznosikov, A. V. Gasnikov, “Local SGD for Near-Quadratic Problems: Improving Convergence under Unconstrained Noise Conditions”, UMN, 2024 (to appear) ; (to appear)
2.
A. V. Gasnikov, V. N. Temlyakov, “On greedy approximation in complex Banach spaces”, UMN, 2024 (to appear) ; (to appear)
3.
A. V. Gasnikov, A. I. Lobanov, Y. A. Kholodov, A. V. Schuplev, M. V. Yashina, “Editor’s note”, Computer Research and Modeling, 16:1 (2024), 5–10
2023
4.
Ya. D. Tominin, V. D. Tominin, E. D. Borodich, D. A. Kovalev, P. E. Dvurechenskii, A. V. Gasnikov, S. V. Chukanov, “On accelerated methods for saddle-point problems with composite structure”, Kompyuternye issledovaniya i modelirovanie, 15:2 (2023), 433–467;
Evgeniya V. Gasnikova, Alexander V. Gasnikov, Demyan V. Yarmoshik, Meruza B. Kubentayeva, Mikhail I. Persiianov, Irina V. Podlipnova, Ekaterina V. Kotlyarova, Ilya A. Sklonin, Elena D. Podobnaya, Vladislav V. Matyukhin, “About multistage transportation model and sufficient conditions for its potentiality”, Mat. Teor. Igr Pril., 15:2 (2023), 3–17
6.
M. S. Alkousa, A. V. Gasnikov, E. L. Gladin, I. A. Kuruzov, D. A. Pasechnyuk, F. S. Stonyakin, “Solving strongly convex-concave composite saddle-point problems with low dimension of one group of variable”, Sb. Math., 214:3 (2023), 285–333
7.
S. S. Ablaev, F. S. Stonyakin, M. S. Alkousa, A. V. Gasnikov, “Adaptive subgradient methods for mathematical programming problems with quasi-convex functions”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S1–S18
8.
B. A. Alashkar, A. V. Gasnikov, D. M. Dvinskikh, A. V. Lobanov, “Gradient-free federated learning methods with $l_1$ and $l_2$-randomization for non-smooth convex stochastic optimization problems”, Comput. Math. Math. Phys., 63:9 (2023), 1600–1653
9.
A. N. Beznosikov, A. V. Gasnikov, K. E. Zainullina, A. Yu. Maslovskii, D. A. Pasechnyuk, “A unified analysis of variational inequality methods: variance reduction, sampling, quantization, and coordinate descent”, Comput. Math. Math. Phys., 63:2 (2023), 147–174
10.
N. T. Nguyen, A. Rogozin, D. Metelev, A. Gasnikov, “Min-max optimization over slowly time-varying graphs”, Dokl. Math., 108:suppl. 2 (2023), S300–S309
11.
M. I. Rudakov, A. N. Beznosikov, Y. A. Kholodov, A. V. Gasnikov, “Activations and gradients compression for model-parallel training”, Dokl. Math., 108:suppl. 2 (2023), S272–S281
12.
D. Medyakov, G. Molodtsov, A. Beznosikov, A. Gasnikov, “Optimal data splitting in distributed optimization for machine learning”, Dokl. Math., 108:suppl. 2 (2023), S465–S475
13.
A. Pichugin, M. Pechin, A. Beznosikov, A. Savchenko, A. Gasnikov, “Optimal analysis of method with batching for monotone stochastic finite-sum variational inequalities”, Dokl. Math., 108:suppl. 2 (2023), S348–S359
14.
A. V. Gasnikov, “Boris Polyak — path in science. Optimization”, Computer Research and Modeling, 15:2 (2023), 235–243
15.
A. V. Gasnikov, A. I. Lobanov, “Editor’s note”, Computer Research and Modeling, 15:2 (2023), 229–233
2022
16.
N. V. Pletnev, P. E. Dvurechenskii, A. V. Gasnikov, “Application of gradient optimization methods to solve the Cauchy problem for the Helmholtz equation”, Computer Research and Modeling, 14:2 (2022), 417–444
17.
P. A. Ostroukhov, R. A. Kamalov, P. E. Dvurechenskii, A. V. Gasnikov, “Tensor methods for strongly convex strongly concave saddle point problems and strongly monotone variational inequalities”, Kompyuternye issledovaniya i modelirovanie, 14:2 (2022), 357–376;
18.
D. M. Dvinskikh, V. V. Pirau, A. V. Gasnikov, “On the relations of stochastic convex optimization problems with empirical risk minimization problems on p-norm balls”, Computer Research and Modeling, 14:2 (2022), 309–319
19.
A. I. Bazarova, A. N. Beznosikov, A. V. Gasnikov, “Linearly convergent gradient-free methods for minimization of parabolic approximation”, Kompyuternye issledovaniya i modelirovanie, 14:2 (2022), 239–255;
M. S. Alkousa, A. V. Gasnikov, P. E. Dvurechenskii, A. A. Sadiev, L. Ya. Razouk, “An approach for the nonconvex uniformly concave structured saddle point problem”, Kompyuternye issledovaniya i modelirovanie, 14:2 (2022), 225–237;
D. Yu. Turdakov, A. I. Avetisyan, K. V. Arkhipenko, A. V. Antsiferova, D. S. Vatolin, S. S. Volkov, A. V. Gasnikov, D. A. Devyatkin, M. D. Drobyshevskiy, A. P. Kovalenko, M. I. Krivonosov, N. V. Lukashevich, V. A. Malykh, S. I. Nikolenko, I. V. Oseledets, A. I. Perminov, I. V. Sochenkov, M. M. Tihomirov, A. N. Fedotov, M. Yu. Khachay, “Trusted artificial intelligence: challenges and promising solutions”, Dokl. Math., 106:suppl. 1 (2022), S9–S13
22.
E. L. Gladin, A. V. Gasnikov, E. S. Ermakova, “Vaidya's Method for Convex Stochastic Optimization Problems in Small Dimension”, Math. Notes, 112:2 (2022), 183–190
23.
A. V. Gasnikov, A. I. Lobanov, “Editor’s note”, Computer Research and Modeling, 14:2 (2022), 209–212
2021
24.
E. L. Gladin, M. Alkousa, A. V. Gasnikov, “Solving convex min-min problems with smoothness and strong convexity in one group of variables and low dimension in the other”, Autom. Remote Control, 82:10 (2021), 1679–1691
25.
E. V. Kotlyarova, A. V. Gasnikov, E. V. Gasnikova, D. V. Yarmoshik, “Finding equilibrium in two-stage traffic assignment model”, Computer Research and Modeling, 13:2 (2021), 365–379
26.
E. A. Vorontsova, A. V. Gasnikov, P. E. Dvurechenskii, A. S. Ivanova, D. A. Pasechnyuk, “Numerical methods for the resource allocation problem in a computer network”, Comput. Math. Math. Phys., 61:2 (2021), 297–328
27.
A. V. Gasnikov, D. M. Dvinskikh, P. E. Dvurechenskii, D. Kamzolov, V. V. Matyukhin, D. A. Pasechnyuk, N. K. Tupitsa, A. V. Chernov, “Accelerated meta-algorithm for convex optimization problems”, Comput. Math. Math. Phys., 61:1 (2021), 17–28
2020
28.
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”, Kompyuternye issledovaniya i modelirovanie, 12:2 (2020), 301–317;
D. M. Dvinskikh, S. S. Omelchenko, A. V. Gasnikov, A. I. Turin, “Accelerated gradient sliding for minimizing a sum of functions”, Dokl. Math., 101:3 (2020), 244–246
30.
D. M. Dvinskikh, A. I. Turin, A. V. Gasnikov, S. S. Omelchenko, “Accelerated and Unaccelerated Stochastic Gradient Descent in Model Generality”, Math. Notes, 108:4 (2020), 511–522
31.
M. S. Alkousa, A. V. Gasnikov, D. M. Dvinskikh, D. A. Kovalev, F. S. Stonyakin, “Accelerated methods for saddle-point problem”, Comput. Math. Math. Phys., 60:11 (2020), 1787–1809
2019
32.
E. Vorontsova, A. V. Gasnikov, E. A. Gorbunov, P. E. Dvurechenskii, “Accelerated gradient-free optimization methods with a non-Euclidean proximal operator”, Autom. Remote Control, 80:8 (2019), 1487–1501
33.
E. A. Vorontsova, A. V. Gasnikov, E. A. Gorbunov, “Accelerated descent along a random direction with non-Euclidean prox-structure”, Avtomat. i Telemekh., 2019, no. 4, 126–143
34.
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”, Math. Notes, 106:1 (2019), 11–19
35.
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”, Num. Anal. Appl., 12:4 (2019), 338–358
36.
A. S. Anikin, O. A. Bol'shakova, A. V. Gasnikov, A. Yu. Gornov, T. V. Ermak, D. V. Makarenko, V. P. Morozov, B. O. Neterebskii, P. A. Yakovlev, “Local algorithms for minimizing the force field for 3D representation of macromolecules”, Comput. Math. Math. Phys., 59:12 (2019), 1994–2008
37.
A. V. Gasnikov, A. I. Turin, “Fast gradient descent for convex minimization problems with an oracle producing a $(\delta,L)$-model of function at the requested point”, Comput. Math. Math. Phys., 59:7 (2019), 1085–1097
38.
A. V. Gasnikov, P. E. Dvurechenskii, F. S. Stonyakin, A. A. Titov, “An adaptive proximal method for variational inequalities”, Comput. Math. Math. Phys., 59:5 (2019), 836–841
39.
D. R. Baymurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechenskii, E. I. Ershov, M. B. Kubentayeva, A. A. Lagunovskaya, “Universal method of searching for equilibria and stochastic equilibria in transportation networks”, Comput. Math. Math. Phys., 59:1 (2019), 19–33
2018
40.
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”, Autom. Remote Control, 79:8 (2018), 1399–1408
41.
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
42.
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
43.
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
44.
P. Dvurechensky, A. Gasnikov, A. Lagunovskaya, “Parallel algorithms and probability of large deviation for stochastic convex optimization problems”, Num. Anal. Appl., 11:1 (2018), 33–37
45.
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”, Num. Anal. Appl., 11:1 (2018), 16–32
46.
A. S. Bayandina, A. V. Gasnikov, E. V. Gasnikova, S. V. Matsievskii, “Primal-dual mirror descent method for constraint stochastic optimization problems”, Comput. Math. Math. Phys., 58:11 (2018), 1728–1736
47.
A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, “Dual methods for finding equilibriums in mixed models of flow distribution in large transportation networks”, Comput. Math. Math. Phys., 58:9 (2018), 1395–1403
48.
A. V. Gasnikov, Yu. E. Nesterov, “Universal method for stochastic composite optimization problems”, Comput. Math. Math. Phys., 58:1 (2018), 48–64
49.
A. V. Gasnikov, A. I. Lobanov, Ya. A. Kholodov, “Editor's note”, Computer Research and Modeling, 10:3 (2018), 279–283
2017
50.
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”, Autom. Remote Control, 78:2 (2017), 224–234
51.
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”, Num. Anal. Appl., 10:4 (2017), 299–312
52.
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”, Comput. Math. Math. Phys., 57:8 (2017), 1262–1276
2016
53.
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”, Autom. Remote Control, 77:11 (2016), 2018–2034
54.
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
55.
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
56.
A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, A. V. Chernov, “Efficient numerical methods for entropy-linear programming problems”, Comput. Math. Math. Phys., 56:4 (2016), 514–524
2015
57.
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
58.
A. V. Gasnikov, Yu. E. Nesterov, V. G. Spokoiny, “On the efficiency of a randomized mirror descent algorithm in online optimization problems”, Comput. Math. Math. Phys., 55:4 (2015), 580–596
59.
A. V. Gasnikov, D. Yu. Dmitriev, “On efficient randomized algorithms for finding the PageRank vector”, Comput. Math. Math. Phys., 55:3 (2015), 349–365
2014
60.
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
61.
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”, Math. Notes, 94:6 (2013), 854–861
62.
A. Gasnikov, Yu. Dorn, E. Nurminskii, N. Shamrai, Kvant, 2013, no. 1, 13–18
2012
63.
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”, Comput. Math. Math. Phys., 52:6 (2012), 937–939
64.
A. Gasnikov, E. Chernousova, T. Nagapetyan, O. Fed'ko, Mat. Pros., 16, MCCME, Moscow, 2012, 181–213
2011
65.
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
66.
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. Math., 73:6 (2009), 1111–1148
2008
67.
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”, Comput. Math. Math. Phys., 48:8 (2008), 1376–1405
2006
68.
A. V. Gasnikov, “Time asymptotic behavior of the solution to a quasilinear parabolic equation”, Comput. Math. Math. Phys., 46:12 (2006), 2136–2153
Presentations in Math-Net.Ru
1.
Conference Opening Alexander Gasnikov AI Autumn School on Computational Optimization (ASCOMP 2024) October 7, 2024 09:55
On decentralized nonsmooth optimization S. Chezhegov, A. V. Gasnikov, A. V. Rogozin The ninth international conference "Quasilinear Equations, Inverse Problems and their Applications" (QIPA 2023) December 4, 2023 16:15
2024
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