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## Primal-Dual Method for Searching Equilibrium in Hierarchical Congestion Population Games

С. 584-595.

Dvurechensky P., Gasnikov A., Gasnikova E., Matsievsky S., Rodomanov A., Usik I.

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 is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity.

Keywords: entropyэнтропияequilibriumсложность алгоритмаравновесиедвойственная задачаdual problemвыпуклая оптимизацияalgorithm complexityprimal-dual methodlogit dynamicsmultistage model of traffic flowsпрямо-двойственный методлогит-динамикамногостадийная модель транспортных потоковconvex optimization

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Vol. 1623. , CEUR Workshop Proceedings, 2016

Puzachenko Y. G., Sandlerskiy R., Sankovski A. G., Entropy 2013 Vol. 15 No. 9 P. 3970-3982

The paper discusses methods of evaluating thermodynamic properties of landscape cover based on multi-spectral measurements by the Landsat satellites. Authors demonstrate how these methods could be used for studying functionality of landscapes and for spatial interpolation of Flux NET system measurements. ...

Added: March 27, 2022

Kiyatkina A., Shadrikov V., Вестник Ярославского государственного университета им. П.Г. Демидова. Серия Гуманитарные науки 2021 Т. 5 № 3 С. 434-443

The article discusses understanding as a human tendency to remove uncertainty through the phenomenon of «entropy». The learning process initially puts the student in a situation of constant movement from a disordered
environment to an ordered one, which occurs due to the constant interruption of the student’s inner world balance. Studies of understanding through entropy allow ...

Added: November 10, 2021

Apenko S.M., Physica A: Statistical Mechanics and its Applications 2012 Vol. 391 No. 1-2 P. 62-77

We present a possible approach to the study of the renormalization group (RG) flow based
entirely on the information theory. The average information loss under a single step of
Wilsonian RG transformation is evaluated as a conditional entropy of the fast variables,
which are integrated out, when the slow ones are held fixed. Its positivity results in the
monotonic ...

Added: October 23, 2014

Rubchinskiy A., , in : Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics. Vol. 197.: Springer, 2017. P. 127-152.

A new approach to network decomposition problems (and, hence, to classification problems, presented in network form) is suggested. Opposite to the conventional approach, consisting in construction of one, “the most correct” decomposition (classification), the suggested approach is focused on construction of a family of classifications. Basing on this family, two numerical indices are introduced and ...

Added: October 20, 2017

Matveenko V. D., Korolev A. V., Математическая теория игр и ее приложения 2011 Т. 3 № 2 С. 50-80

A contract theory model is studied in which objective functions of a regulator and of two types of firms include ecological variables. It is shown that the choice of a way of functioning of the regulating mechanism (separating or pooling) depends both on political conditions (what kind of regulator defines the mechanism and the contracts) ...

Added: November 17, 2012

Bezhaeva Z., Oseledets V. I., Journal of Dynamical and Control Systems 2013 Vol. 19 No. 2 P. 301-308

Consider a sofic dynamical system. We obtain an explcit formula for the KS-entropy of sofic dynamicsl system of Blackwell's type. ...

Added: August 22, 2013

Zhukova G., Сметанин Ю. Г., Ulyanov M., , in : 2019 International Conference on Engineering Technologies and Computer Science (EnT). : IEEE, 2019. P. 43-47.

A qualitative analysis refers to the identification of the qualitative characteristics of a time series, such as its periodicity, final periodicity or near periodicity, convergence to the limit state, randomness, etc. For such an analysis, methods of symbolic dynamics are used, with the time series being represented as a sequence of symbols from a finite ...

Added: October 22, 2019

Maksim D. Miroshnichenko, Russian Studies in Philosophy 2022 Vol. 60 No. 3 P. 205-230

The paper reconstructs the conception of the Soviet-American psychologist Vladimir Lefebvre as part of the neocybernetic movement. In particular, I propose to consider such components of his research of the 70s-90s as systemic vision, reflexive analysis, search for a holistic configuration, and Janus-cosmology as realizations of neocybernetics. Lefebvre's interest in the reflexive structures of cognition ...

Added: November 29, 2021

Bezhaeva Z., Oseledets V. I., Functional Analysis and Its Applications 2010 Vol. 44 No. 2 P. 83-91

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. ...

Added: April 12, 2012

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

Быкадоров И.А., Желободько Е.В., Коковин С.Г., В кн. : XII Международная научная конференция по проблемам развития экономики и общества. В четырех книгах. Книга 3. Кн. 3.: М. : Издательский дом НИУ ВШЭ, 2012. С. 512-520.

С начала XXI века Россия и другие развивающиеся рынки бывшего СССР демонстрируют бурный рост крупных торговых сетей в потребительском секторе. Трейдеры захватили большую долю рынка и получили значительную рыночную силу. Это изменение рыночной организации может привести к негативным последствиям для общественного благосостояния, ассортимента благ и инфляции. Общественный интерес к этому вопросу привел к дебатам в ...

Added: November 17, 2013

Sandlersky Robert, Krenke Alexander, Entropy 2020 Vol. 22 No. 10 Article 1132

The hypothesis of an increase in free energy (exergy) by ecosystems during evolution is tested on direct measurements. As a measuring system of thermodynamic parameters (exergy, information, entropy), a series of measurements of reflected solar radiation in bands of Landsat multispectral imagery for 20 years is used. The thermodynamic parameters are compared for different types ...

Added: March 21, 2022

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

Gromoff A., Bilinkis (Stavenko) J., Информационные технологии в проектировании и производстве 2011 № 3 С. 28-35

This article discusses and applies an approach to solution of business process monitoring task on the basis of study of entropy characters of an acting business system information field, which is considered from a view of behavior and modeling of open systems. Process flow continuity in time is taken to account. A method of stability ...

Added: December 10, 2012

Rubchinskiy A., / Высшая школа экономики. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2015. No. WP7/2015/09.

An algorithm of solution of the Automatic Classification (AC for brevity) problem is set forth in the paper. In the AC problem, it is required to find one or several partitions, starting with the given pattern matrix or dissimilarity / similarity matrix. The three-level scheme of the algorithm is suggested. The output of the procedure ...

Added: October 19, 2017

Skripchenko A., Troubetzkoy S., / Cornell University. Series math "arxiv.org". 2015. No. 1501.04584.

We prove that a polygonal billiard with one-sided mirrors has zero
topological entropy. In certain cases we show sub exponential and for other
polynomial estimates on the complexity. ...

Added: January 26, 2015

Fridman A., Вербецкий А. Д., Экономическая политика 2014 № 6 С. 137-160

The paper focuses on the specifics of government regulation of higher education market in Russia. We propose a theoretical model of price competition between universities under vertical differentiation, where each university provides services in accordance with state-funded quota and sets the price for the services produced above this quota. It is shown that efficient allocation ...

Added: January 12, 2015

Popkov Y., Popkov A., Dubnov Y. A., Автоматика и телемеханика 2020 № 7 С. 148-172

A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...

Added: October 31, 2020

Bezhaeva Z., Oseledets V. I., / The Erwin Schrodinger International Institute for Mathematical Physics. Series "ESI preprints". 2008. No. 2087.

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. ...

Added: April 12, 2012

Bilinkis (Stavenko) J., Gromoff A., Качество. Инновации. Образование 2012 № 7 С. 80-87

The article includes an example of a system approach to managing operational risk in the procurement process. According this approach, 4 interrelated subsystems were identified: beliefs, constraints, control and monitoring. Therefore the operational risk management is a Meta process embedded into business processes and set requirements to the above subsystems. ...

Added: December 13, 2012

Sorvin K., В кн. : Самосознание: мое и наше. : М. : ИФРАН, 1997. С. 153-211.

Added: June 21, 2015

В.Н. Азаров, Бойцов Б. В., Ю.И. Гудков et al., Компетентность 2017 № 9-10 С. 46-57

We have examined the main new competencies that should be matched by the specialist — managers of complex techno-technological and socio-economic systems in the era of information (digital) and industrial revolutions. We have also investigated what kind of overprofessional competencies the expert should have and what the system of its preparation includes. Having outlined and ...

Added: January 29, 2018

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

Beznosikov A., Richtarik P., Diskin M. et al., , in : Thirty-Sixth Conference on Neural Information Processing Systems : NeurIPS 2022. : Curran Associates, Inc., 2022. P. 14013-14029.

Added: January 27, 2023