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## Markov Decision Processes and Stochastic Games with Total Effective Payoff

P. 103-115.

We consider finite Markov decision processes (MDPs) with undiscounted total effective payoff. We show that there exist uniformly optimal pure stationary strategies that can be computed by solving a polynomial number of linear programs. We apply this result to two-player zero-sum stochastic games with perfect information and undiscounted total effective payoff, and derive the existence of a saddle point in uniformly optimal pure stationary strategies.

### In book

Vol. 30. , Dagstuhl : Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2015

Belenky A., Egorova L. G., / Издательский дом ВШЭ. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2015. No. WP7/2015/02.

Two mathematical models formalizing the decision-making process by a trader on developing and changing her investment portfolio in a stock exchange are presented. According to the first model the trader can correctly predict future values of financial securities of her interest. In this case, the problem of finding optimal strategies of investing in these financial ...

Added: May 31, 2015

Liverpool : Luniver Pre, 2011

World leading experts give their accounts of the modern mathematical models in the field: Markov Decision Processes, controlled diffusions, piece-wise deterministic processes etc, with a wide range of performance functionals. One of the aims is to give a general view on the state-of-the-art. The authors use Dynamic Programming, Convex Analytic Approach, several numerical methods, index-based ...

Added: April 12, 2012

Tamm M., Valba O. V., Nechaev S., Journal of Physics A: Mathematical and Theoretical 2011 Vol. 44 P. 195001

A new statistical approach to alignment (finding the longest common subsequence) of two random RNA-type sequences is proposed. We have constructed a generalized ‘dynamic programming’ algorithm for finding the extreme value of the free energy of two noncoding RNAs. In our procedure, we take into account the binding free energy of two random heteropolymer chains ...

Added: November 19, 2013

Belenky A., Procedia Computer Science 2014 Vol. 31 P. 1150-1159

A part of a country’s electrical grid in which an electricity generator (which may consist of several base load power plants
and several peaking power plants) supplies electricity to a set of large customers of the grid, whereas the customers can a)
receive electricity from renewable sources of energy, b) store electricity in certain volumes, and c) ...

Added: September 29, 2014

Belenky A., International Journal of Public Administration 2018

An approach to calculating an economically optimal composition of powers of the plants for processing fractions of large city's municipal solid waste (MSW) disposed of in the landfills surrounding the city into various useful products is proposed. This environmental management problem is considered under a limited city's budget and uncertainties on the a) city's MSW ...

Added: November 1, 2018

Belenky A., Egorova L. G., , in : Advances in Intelligent Systems and Computing. Issue 359: Modelling, Computation and Optimization in Information Systems and Management Sciences.: Switzerland : Springer, 2015. P. 257-268.

The paper discusses a new approach to developing tools for quantitatively analyzing the financial behavior of small and medium price-taking traders each possessing abilities to predict share price values for a set of financial securities traded in a stock exchange. Tools for forming and managing a trader’s portfolio of securities from this set are proposed. ...

Added: June 1, 2015

Гурарий М. М., Жаров М. М., Русаков С. Г. et al., Информационные технологии 2018 Т. 24 № 7 С. 435-444

The directions of improvement of minimax methods for circuit design problems are considered. The choices of generalized quality criterion for the circuit design is discussed. It is concluded that the minimax criterion has advantages over other formulations of design targets. New approach to setting of individual objectives for each performance indicator is proposed. The approach ...

Added: February 12, 2019

Valba O. V., Nechaev S., Tamm M., Журнал экспериментальной и теоретической физики 2012 Т. 141 С. 399

В данной работе предлагается новый статистический подход для решения задачи сравнения (``выравнивания'') двух последовательностей РНК. Данная проблема рассматривается с точки зрения связывания двух взаимодействующих полимеров, имеющих сложную иерархическую кактусообразную структуру характерную для молекул РНК. Выравнивание двух последовательностей характерезуется числом совпадающих и несовпадающих букв, а также числом пропусков (\glqq делеций\grqq). Для каждого выравнивания определяется \glqq весовая ...

Added: November 19, 2013

Belenky A., Egorova L. G., / Издательский дом ВШЭ. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2016. No. 02.

The paper presents two new approaches to modeling the interaction of small and medium price-taking traders with a stock exchange. In the framework of these approaches, the traders can form and manage their portfolios of financial instruments traded on a stock exchange with the use of linear, integer, and mixed programming techniques. Unlike previous authors’ ...

Added: June 27, 2016

Маршалко Г. Б., Математические вопросы криптографии 2014 Vol. 5 No. 2 P. 87-98

We show that neuron weights used in neural network-based biometric authentication scheme defined in GOST R 52633 standard series contain all the information on biometric data and secret key of the legitimate user. So, the complexity of evaluating (with known tables of neuron weights) the legitimate user's secret key is equivalent to the complexity of evaluating ...

Added: October 7, 2022

Kashtanov V., Зайцева О. Б., М. : КУРС: ИНФРА-М, 2016

Contents of the book is divided into 2 parts of deterministic and stochastic models of Operations Research.
The first part of "Deterministic models of Operations Research" - is the base section, in which the emphasis is on linear programming.
The second part - "Stochastic models of Operations Research" includes a model of reliability and queuing models. This ...

Added: November 13, 2016

Lazarev A. A., Pravdivets N., Nekrasov I., Algorithms 2018 Vol. 11 No. 4 P. 1-13

We consider one approach to formalize the Resource-Constrained Project Scheduling Problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original problem into combinatorial setting is based on interpreting each operation as an atomic entity that has a defined duration and has to be resided on the continuous time axis meeting additional restrictions. ...

Added: October 1, 2018

Gurvich V., Boros E., Elbassioni K. et al., Dynamic Games and Applications 2018 Vol. 8 No. 1 P. 22-41

We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real εε, let us call a stochastic game εε-ergodic, if its values from any two initial positions differ by at most εε. The proposed new algorithm outputs for every ε>0ε>0 in finite time either a pair of stationary strategies for the two ...

Added: October 10, 2018

Belenky A., Applied Mathematics Letters 2007 Vol. 20 No. 7 P. 795-799

The maximin of a function being the minimum function of a sum of two bilinear functions with one and the same first vector argument belonging to a polyhedron is considered on a polyhedron of connected variables forming two second vector arguments of the bilinear functions. It is shown that finding the exact lower estimate of ...

Added: October 21, 2016

Kolesnikov A., Zaev D., / Cornell University. Series math "arxiv.org". 2013.

We consider probability measures on $\mathbb{R}^{\infty}$ and study natural analogs of optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric properties, in particular, exchangeable and stationary measures. It turns out that the existence problem for optimal transportation is closely related to various ergodic ...

Added: May 13, 2013

Boros E., Elbassioni K., Gurvich V. et al., Optimization Letters 2017 Vol. 11 No. 8 P. 1499-1512

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph (Formula presented.), with local rewards (Formula presented.), and three types of positions: black (Formula presented.), white (Formula presented.), and random (Formula presented.) forming a partition of V. It is a long-standing open question whether a polynomial time algorithm ...

Added: May 18, 2017

Chemodanov D., Esposito F., Calyam P. et al., IEEE Transactions on Network and Service Management 2019 Vol. 16 No. 1 P. 127-142

Virtual network services that span multiple data centers are important to support emerging data-intensive applications in fields such as bioinformatics and retail analytics. Successful virtual network service composition and maintenance requires flexible and scalable “constrained shortest path management” both in the management plane for virtual network embedding (VNE) or network function virtualization service chaining (NFV-SC), ...

Added: December 3, 2019

Mikheev A. V., В кн. : Современное образование: содержание, технологии, качество. Материалы XXIV международной научно-методической конференции. Т. 2.: СПб. : Издательство СПбГЭТУ "ЛЭТИ", 2018. С. 55-56.

The issue of using the MathCAD software package in a university educational course for learning to solve optimization problems is considered. The advantage of working with this program is shown and its main features are discussed in the appendix to this course. ...

Added: April 24, 2018

Sokolov A. V., Tokarev V. V., М. : Физматлит, 2012

The manual is devoted to the mathematical theory and methods of optimization applied to administrative decisions in economy. Volume 1 described approaches to mathematical modeling of management problems in economy and methods of mathematical programming tasks solution. Besides strict mathematical proofs, there are directing reasons, which is sometimes enough for understanding. There are many economic ...

Added: November 25, 2013