### ?

## Distributed Methods with Compressed Communication for Solving Variational Inequalities, with Theoretical Guarantees

P. 14013-14029.

### In book

Curran Associates, Inc., 2022

Chernikov B. V., Информатика и ее применения 2009 Т. 3 № 4 С. 64-75

The technology of storage of poorly formalized documents that are created using lexicological synthesis is considered. The technology provides formation of the kept index sequences containing indexes of document forms and their substantial components. Additionally, thanks to simultaneous preparation of documents and creation of kept index sequences, the economy of time is provided. The experiments ...

Added: November 26, 2012

Ingacheva A., Кохан В. В., Ershov E. et al., Сенсорные системы 2018 Т. 32 № 4 С. 332-341

In this paper we consider the task of inner objects mapping for the building with a bunch of moving around it autonomous agents which use narrow beam of radio waves using WiFi frequency (2.4 GHz). Linear model of pixel-wise radio waves attenuation is considered. SIRT algorithm with TV and Tikhonov regularizations is used for the ...

Added: February 9, 2020

Puzino Y. A., Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния 2014 № 22 С. 46-52

The increasing of the efficiency of technological modes of steel products manufacturing requires simulation of metal forming during hot deformation. To obtain correct results, one should set the correct initial and boundary conditions, including the mechanical properties of materials, which represent the dependence of the stress-strain and strain rate at maintained temperature.
In the experiments one ...

Added: January 19, 2015

Kovalev D., Shulgin E., Richtarik P. et al., PMLR, 2021

We propose ADOM – an accelerated method for smooth and strongly convex decentralized optimization over time-varying networks. ADOM uses a dual oracle, i.e., we assume access to the gradient of the Fenchel conjugate of the individual loss functions. Up to a constant factor, which depends on the network structure only, its communication complexity is the ...

Added: October 31, 2021

Ivanova A., Пасечнюк Д., Dvurechensky P. et al., / Cornell University. Серия "Working papers by Cornell University". 2019.

In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem, which we consider is a maximization problem with linear inequality constraints. To solve this problem we construct the dual problem and propose to use ...

Added: October 23, 2020

Bogachev T., / Cornell University. Series math "arxiv.org". 2022.

In this research a continuous model for resource allocations in a queuing system is considered and a local prediction on the system behavior is developed. As a result we obtain a set of possible cases, some of which lead to quite clear optimization problems. Currently, the main result of this research direction is an algorithm ...

Added: October 21, 2022

Puchkin N., Gorbunov E., Kutuzov N. et al., , in : Proceedings of The 27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024), 2-4 May 2024, Palau de Congressos, Valencia, Spain. PMLR: Volume 238. Vol. 238.: Valencia : PMLR, 2024. P. 856-864.

We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than 𝑂(𝐾^{−2(𝛼−1)/𝛼}), when the stochastic gradients have finite 𝛼-th moment, 𝛼∈(1,2]. In particular, our analysis allows the noise norm to have an unbounded expectation. To achieve these results, we stabilize stochastic gradients, ...

Added: April 22, 2024

Dvurechensky P., Gasnikov A., Gasnikova E. et al., В кн. : Proceedings of DOOR 2016 Conference, special issue of CEUR Workshop Proceedings. Vol. 1623.: CEUR Workshop Proceedings, 2016. С. 584-595.

In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization problem. We propose a fast primal-dual composite gradient method and apply it to the problem, which ...

Added: November 17, 2017

Воронцова Е. А., Gasnikov A., Gorbunov E., Автоматика и телемеханика 2019 Т. 80 № 4 С. 126-143

We consider smooth convex optimization problems whose full gradient is not available for their numerical solution. In 2011, Yu.E. Nesterov proposed accelerated gradient-free methods for solving such problems. Since only unconditional optimization problems were considered, Euclidean prox-structures were used. However, if one knows in advance, say, that the solution to the problem is sparse, or ...

Added: October 10, 2020

Ivanova A., Gasnikov A., Dvurechensky P. et al., / Working papers by Cornell University. Series "Optimization and Control". 2020.

Ubiquitous in machine learning regularized empirical risk minimization problems are often composed of several blocks which can be treated using different types of oracles, e.g., full gradient, stochastic gradient or coordinate derivative. Optimal oracle complexity is known and achievable separately for the full gradient case, the stochastic gradient case, etc. We propose a generic framework ...

Added: October 25, 2020

Novikov A., Podoprikhin D., Osokin A. et al., , in : Advances in Neural Information Processing Systems 28 (NIPS 2015). : NY : Curran Associates, 2015.

Deep neural networks currently demonstrate state-of-the-art performance in several domains.At the same time, models of this class are very demanding in terms of computational resources. In particular, a large amount of memory is required by commonly used fully-connected layers, making it hard to use the models on low-end devices and stopping the further increase of ...

Added: February 27, 2017

Osokin A., Alayrac J., Lukasewitz I. et al., , in : Proceedings of Machine Learning Research. Proceedings of the International Conference on Machine Learning (ICML 2016). Vol. 48.: NY : [б.и.], 2016. P. 885-925.

In this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of structured prediction, though it has wider applications. The key intuition behind our improvements is that the estimates of block gaps maintained by ...

Added: October 19, 2017

Чуприн В. И., Rodriges Zalipynis R. A., В кн. : Научные труды Донецкого национального технического университета. Серия: системный анализ и информационные технологии в науках о природе и обществе. Issue 1(2)–2(3).: Donetsk : Донецкий национальный технический университет, 2012. С. 192-195.

The paper analyzes storage peculiarities of satellite Earth remote sensing data time
series. We propose methods for their compression based on the discovered peculiarities exploiting
different schemes of Huffman coding. One of the proposed methods reaches 6% increase in the
compression ratio (93%) in contrast to the deflate method used in Java SE6 (87%), for a time
series of ...

Added: October 22, 2015

Puzino Y. A., В кн. : Научно-техническая конференция студентов, аспирантов и молодых специалистов НИУ ВШЭ им. Е.В. Арменского. Материалы конференции. : М. : МИЭМ НИУ ВШЭ, 2015. С. 18-19.

В ходе данной работы была описана математическая модель зависимости «напряжение-деформация» для образцов из стали AISI 304 (аналог 08Х18Н10). Найдены коэффициенты для уравнения состояния данного материала, которые характеризуют зависимость интенсивности напряжений от интенсивности деформации, скорости деформации (0.15, 0.5, 1.5, 5 и 15 сек-1) и температуры (800, 950, 1080 и 1200 градусов). ...

Added: May 19, 2015

Gasnikov A., Баяндина А. С., Лагуновская А. А., Автоматика и телемеханика 2018 № 8 С. 38-49

Изучаются негладкие выпуклые задачи стохастической оптимизации с двухточечным оракулом нулевого порядка, т.е. на каждой итерации наблюдению доступны значения реализации функции в двух выбранных точках. Эти задачи предварительно сглаживаются с помощью известной техники двойного сглаживания (Б. Т. Поляк), а затем решаются с помощью стохастического метода зеркального спуска. Получены условия на допустимый уровень шума неслучайной природы, проявляющегося при вычислении реализации функции, при котором сохраняется ...

Added: October 31, 2018

Sergeev A., Ukhanova A., Forchhammer S., , in : Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7870: IS&T/SPIE ELECTRONIC IMAGING.: United States of America : SPIE, 2011.

JPEG-LS, the well-known international standard for lossless and near-lossless image compression, was originally designed for non-scalable applications. In this paper we propose a scalable modification of JPEG-LS and compare it with the leading image and video coding standards JPEG2000 and H.264/SVC intra for low-complexity constraints of some wireless video applications including graphics. ...

Added: December 3, 2020

Titov A., Stonyakin F., Alkousa M. et al., , in : Mathematical Optimization Theory and Operations Research: Recent Trends: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Revised Selected Papers. : Cham : Springer, 2021. Ch. 6. P. 86-101.

Added: October 26, 2021

Ingacheva A., Kokhan V., Osipov D., , in : Proceedings of the 32nd European Conference on Modelling and Simulation (ECMS 2018),Wilhelmshaven, Germany 22 – 25 May 2018. : NY : Curran Associates, Inc., 2018. P. 183-189.

In this paper we consider the task of inner objects mapping for the building with a bunch of moving around it autonomous agents which use narrow beam of radio waves using WiFi frequency (2.4 GHz). Linear model of pixel-wise radio waves attenuation is considered. SIRT algorithm with TV and Tikhonov regularizations is used for the ...

Added: April 6, 2019

Kornilov N., Shamir O., Lobanov A. et al., , in : Advances in Neural Information Processing Systems 36 (NeurIPS 2023). : Curran Associates, Inc., 2023.

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the batched accelerated gradient method, was proposed in (Gasnikov et. al., 2022). This optimality is defined in terms of iteration and oracle ...

Added: March 26, 2024

Moulines E., Pereyra M., Durmus A., SIAM Journal on Imaging Sciences 2018 Vol. 11 No. 1 P. 473-506

Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimization, which scales very efficiently to high-dimensional image models and delivers accurate point estimation results. However, in order to perform more complex analyses, for example, image uncertainty quantification or model selection, it is ...

Added: December 11, 2018

Dvinskikh D., Gorbunov E., Gasnikov A. et al., , in : 2019 IEEE 58th Conference on Decision and Control (CDC). : IEEE, 2019. P. 7435-7440.

We introduce primal and dual stochastic gradient oracle methods for distributed convex optimization problems over networks. We show that the proposed methods are optimal (in terms of communication steps) for primal and dual oracles. Additionally, for a dual stochastic oracle, we propose a new analysis method for the rate of convergence in terms of duality ...

Added: February 5, 2021

Ivanova A., Dvurechensky P., Vorontsova E. et al., Journal of Optimization Theory and Applications 2022 Vol. 193 No. 1-3 P. 462-490

Many convex optimization problems have structured objective functions written as a sum of functions with different oracle types (e.g., full gradient, coordinate derivative, stochastic gradient) and different arithmetic operations complexity of these oracles. In the strongly convex case, these functions also have different condition numbers that eventually define the iteration complexity of first-order methods and ...

Added: October 28, 2022

Kamzolov D., Dvurechensky P., Gasnikov A., Optimization Methods and Software 2021 Vol. 36 No. 6 P. 1289-1316

In this paper, we propose new first-order methods for minimization of a convex function on a simple convex set. We assume that the objective function is a composite function given as a sum of a simple convex function and a convex function with inexact Hölder-continuous subgradient. We propose Universal Intermediate Gradient Method. Our method enjoys ...

Added: August 4, 2020

Dvurechensky P., Ostroukhov P., Safin K. et al., , in : International Conference on Machine Learning (ICML 2020). Vol. 119.: PMLR, 2020.

Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is much cheaper to implement than projections and some sparsity needs to be preserved. In a number of applications, e.g. Poisson inverse problems ...

Added: October 31, 2020