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Accelerated Gradient-Free Optimization Methods with a Non-Euclidean Proximal Operator
Automation and Remote Control. 2019. Vol. 80. No. 8. P. 1487-1501.
We propose an accelerated gradient-free method with a non-Euclidean proximal operator associated with the p-norm (1 ⩽ p ⩽ 2). We obtain estimates for the rate of convergence of the method under low noise arising in the calculation of the function value. We present the results of computational experiments.
Nesterov Y., Gasnikov A., Guminov S. et al., Optimization Methods and Software 2021 Vol. 36 No. 4 P. 773-810
In this paper, a new variant of accelerated gradient descent is proposed. The proposed method does not require any information about the objective function, uses exact line search for the practical accelerations of convergence, converges according to the well-known lower bounds for both convex and non-convex objective functions, possesses primal–dual properties and can be applied ...
Added: August 4, 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
Dvurechensky P., Gasnikov A., Journal of Optimization Theory and Applications 2016 Vol. 171 No. 1 P. 121-145
In this paper, we introduce new methods for convex optimization problems with stochastic inexact oracle. Our first method is an extension of the Intermediate Gradient Method proposed by Devolder, Glineur and Nesterov for problems with deterministic inexact oracle. Our method can be applied to problems with composite objective function, both deterministic and stochastic inexactness of ...
Added: October 31, 2020
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
Guminov S., Nesterov Y., Dvurechensky P. et al., Doklady Mathematics 2019 Vol. 99 No. 2 P. 125-128
A new version of accelerated gradient descent is proposed. The method does not require any a priori information on the objective function, uses a linesearch procedure for convergence acceleration in practice, converge according to well-known lower bounds for both convex and nonconvex objective functions, and has primal-dual properties. A universal version of this method is ...
Added: October 31, 2020
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
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
Dvurechensky P., Gasnikov A., Остроухов П. et al., / Working papers by Cornell University. Series "Optimization and Control". 2020.
Motivated by convex problems with linear constraints and, in particular, by entropy-regularized optimal transport, we consider the problem of finding ε-approximate stationary points, i.e. points with the norm of the objective gradient less than ε, of convex functions with Lipschitz p-th order derivatives. Lower complexity bounds for this problem were recently proposed in [Grapiglia and Nesterov, arXiv:1907.07053]. However, the ...
Added: October 25, 2020
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
Bergou E. H., Eduard Gorbunov, Richtarik P., SIAM Journal on Optimization 2020 Vol. 30 No. 4 P. 2726-2749
In this paper we consider the unconstrained minimization problem of a smooth function in $\mathbb{R}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm---the stochastic three points (STP) method---and analyze its iteration complexity. At each iteration, STP generates a random search direction according to a certain fixed probability law. Our ...
Added: November 10, 2020
Ivanova A., Стонякин Ф., Пасечнюк Д. et al., / Working papers by Cornell University. Series "Optimization and Control". 2019.
Network utility maximization is the most important problem in network traffic management. Given the growth of modern communication networks, we consider the utility maximization problem in a network with a large number of connections (links) that are used by a huge number of users. To solve this problem an adaptive mirror descent algorithm for many ...
Added: October 25, 2020
Rodomanov A., Kropotov D., SIAM Journal on Optimization 2020 Vol. 30 No. 3 P. 1878-1904
We analyze the coordinate descent method with a new coordinate selection strategy, called volume sampling. This strategy prescribes selecting subsets of variables of certain size proportionally to the determinants of principal submatrices of the matrix, which bounds the curvature of the objective function. In the particular case when the size of the subsets equals one, ...
Added: July 29, 2020
Dvurechensky P., Eduard Gorbunov, Gasnikov A., European Journal of Operational Research 2021 Vol. 290 No. 2 P. 601-621
We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be considered as an intermediate one between derivative-free optimization and gradient-based optimization. We assume that at any given point and for any given direction, a stochastic approximation for the directional ...
Added: September 25, 2020
М. : Издательский центр «Российский государственный гуманитарный университет», 2019
Сборник включает 27 докладов международной конференции по компьютерной лингвистике и интеллектуальным технологиям «Диалог 2019», не вошедшие в ежегодник «Компьютерная лингвистика и интеллектуальные технологии», но рекомендованные Программным Комитетом к представлению на конференции. Для специалистов в области теоретической и прикладной лингвистики и интеллектуальных технологий. ...
Added: December 10, 2019
Karpov V. E., Karpova I. P., Procedia Engineering 2015 Vol. 100 P. 1459-1468
Work solutions are proposed for problems of leader definition and role distribution in homogeneous groups of robots. It is shown that transition from a swarm to a collective of robots with hierarchical organization is possible using exclusively local interaction. The local revoting algorithm is central to the procedure for choice of leader while redistribution of roles can ...
Added: March 14, 2015
Chernyshev S. V., Cherepanov E. A., Pankratiev E. V. et al., Journal of Mathematical Sciences 2005 Vol. 128 No. 6 P. 3487-3495
Added: January 27, 2014
Chuprikov P., Nikolenko S. I., Davydow A. et al., IEEE Transactions on Networking 2018 Vol. 26 No. 1 P. 342-355
Modern network elements are increasingly required to deal with heterogeneous traffic. Recent works consider processing policies for buffers that hold packets with different processing requirements (number of processing cycles needed before a packet can be transmitted out) but uniform value, aiming to maximize the throughput, i.e., the number of transmitted packets. Other developments deal with ...
Added: March 14, 2018
Sotnikova S., Динамика сложных систем 2012 № 3 С. 84-87
In article is described designed programme complex of the physical processes modeling, which also allows to conduct the identification printed node parameters (the physical model). On printed node designed the on-board secondary power supply source is realized. For it are designed relationship interfaces of controlling program with the known program of modeling and optimization. ...
Added: December 5, 2014
Skoptsov K. A., Sheshenin S., Galatenko V. V. et al., International Journal of Applied Mechanics 2016 Vol. 8 No. 2 P. 1650016-01-1650016-18
We present a method for evaluating elastic properties of a composite material produced by molding a resin filled with short elastic fibers. A flow of the filled resin is simulated numerically using a mesh-free method. After that, assuming that spatial distribution and orientation of fibers are not significantly changed during polymerization, effective elastic moduli of ...
Added: May 22, 2016
Malyshev D., Discrete Mathematics 2015 Vol. 338 No. 11 P. 1860-1865
We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. ...
Added: April 7, 2014
Каз. : Издательство «Фэн» Академии наук Республики Татарстан, 2013
Материалы и доклады Шестой Всероссийской научно-практической конференции по имитацонному моделированию и его применению в науке и промышленности. ...
Added: December 14, 2013
Borchmann D., Hanika T., Obiedkov S., Discrete Applied Mathematics 2020 Vol. 273 P. 30-42
We propose an algorithm for learning the Horn envelope of an arbitrary domain using an expert, or an oracle, capable of answering certain types of queries about this domain. Attribute exploration from formal concept analysis is a procedure that solves this problem, but the number of queries it may ask is exponential in the size ...
Added: October 29, 2019
Goncharov R., Сапанов П. М., Яшунский А. Д., Социология власти 2013 № 3 С. 57-72
В статье представлена технология, позволяющая собирать в полевых исследованиях пространственно локализованные данные об объектах городской среды. Технология основана на автоматической привязке фотографий к пространственным координатам. Приведен план полевых и камеральных мероприятий, предложены варианты ГИС-обработки собираемых таким образом данных. В качестве примера приведены данные об использовании белорусского языка в общественном пространстве городов Белоруссии. ...
Added: April 12, 2015
Springer, 2012
Added: January 29, 2013