• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Finding the exact lower estimate of the maximin of a minimum function on a polyhedron of connected variables
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
July 24, 2026
‘I Like Self-Fulfilling Prophecies
Andrey Vorchik studies happiness, delivers popular science lectures, and believes that science should address social issues as well. In an interview for the Young Scientists of HSE University project, he spoke about how emotions influence decision-making, the Bermuda Triangle formed by the bathroom, refrigerator, and bed, and the ideal formula for education.
July 24, 2026
'Physics Is What the World Is Literally Built On'
Physicist Nina Dzhanayeva, recipient of a Vladimir Potanin Foundation scholarship, focuses her research on nanophotonics. In this interview for the HSE Young Scientists project, she discusses nanowells, scientific intuition, and how physics can help in making frangipane cream puffs.
July 20, 2026
Scientists Create Open Dataset for Studying Concentration
A team of Russian researchers, including scientists from HSE University–St Petersburg, has developed the first open multimodal dataset containing recordings of brain activity, heart function, and video observations to help researchers understand what happens in the human brain during deep concentration. In the future, the dataset could accelerate the development of neural interfaces, rehabilitation technologies, and AI systems. The article has been published in Scientific Data.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Finding the exact lower estimate of the maximin of a minimum function on a polyhedron of connected variables

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

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 this maximin is reducible to solving a quadratic programming problem.

Language: English
DOI
Text on another site
Keywords: linear programmingConnected variablesMaximin problems
Similar publications
On the problem of optimal fair exchange
Kolesnikov A., Popova S., / Series arXiv "math". 2024.
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the optimal exchange problem are proved in case of completely regular topological spaces. We show the connection between the problem of optimal exchange and the optimal ...
Added: December 20, 2024
Обзор выпуклой оптимизации марковских процессов принятия решений
Rudenko V., Yudin N., Васин А. А., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 329–353
This article reviews both historical achievements and modern results in the field of Markov Decision Process (MDP) and convex optimization. This review is the first attempt to cover the field of reinforcement learning in Russian in the context of convex optimization. The fundamental Bellman equation and the criteria of optimality of policy — strategies based on it, ...
Added: November 29, 2024
On a simple connection between Δ-modular ILP and LP, and a new bound on the number of integer vertices
Gribanov D., Malyshev D., Shumilov I., Operations Research Forum 2024 Vol. 5 Article 32
In our note, we present a very simple and short proof of a new interesting fact about the faces of an integer hull of a given rational polyhedron. This fact has a complete analog in linear programming theory and can be useful to establish new constructive upper bounds on the number of vertices in an integer hull of ...
Added: April 4, 2024
Exact Algorithm for Generating H-Cores in Simplified Lattice-Based Protein Model
Ignatov A., , in: 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers. Communications in Computer and Information Science (CCIS, volume 1913)Vol. 1913.: Springer, 2023. P. 173–187.
Modeling protein folding, which is the process by which a protein obtains its spacial shape, still remains a challenging problem. Protein geometry might be simplified by using the coarse-grained models. The highest level of simplification is achieved in HP-models where only polarity of amino acid residues is considered, and the unified monomers are located in nodes ...
Added: January 18, 2024
О безопасности схемы биометрической аутентификации, основанной на нейронной сети
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
A Constrained Shortest Path Scheme for Virtual Network Service Management
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
Минимаксная оптимизация в задачах схемотехнического проектирования
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
Evaluating Typical Algorithms of Combinatorial Optimization to Solve Continuous-Time Based Scheduling Problem
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
Применение программного пакета MathCAD для обучения решению задач линейного программирования
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
Исследование операций. Линейное программирование и стохастические модели.
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
Markov Decision Processes and Stochastic Games with Total Effective Payoff
Gurvich V., Boros E., Elbassioni K. et al., , in: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015), Leibniz International Proceedings in Informatics (LIPIcs)Vol. 30.: Dagstuhl: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2015. 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 ...
Added: October 22, 2016
A mathematical model for estimating the potential margin of state undecided voters for a candidate in a US Federal election
Belenky A., King D. C., Mathematical and Computer Modelling 2007 Vol. 45 No. 5-6 P. 585–593
A US Federal election in which candidates from two major political parties compete for the votes of those undecided voters in a state who usually do not vote in US elections is considered. A mathematical model for evaluating the expectation of the margin of votes to be received from such voters by either candidate as ...
Added: October 21, 2016
The continuity of two function associated with a maximin problem with connected variables
Belenky A., Applied Mathematics Letters 2007 Vol. 20 No. 7 P. 773–777
A function being the sum of two bilinear functions with one and the same first vector argument belonging to a polyhedron and the other two vector arguments belonging to another polyhedron is considered. It is shown that a certain minimum function of this sum and the maximin function of the sum (on the second polyhedron ...
Added: October 21, 2016
Two approaches to modeling the interaction of small and medium price-taking traders with a stock exchange by mathematical programming techniques
Belenky A., Egorova L., / 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
An Approach to Forming and Managing a Portfolio of Financial Securities by Small and Medium Price-Taking Traders in a Stock Exchange
Belenky A., Egorova L., , in: Advances in Intelligent Systems and ComputingIssue 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
Две модели принятия решений участником торгов на фондовой бирже по формированию и изменению своего инвестиционного портфеля
Belenky A., Egorova L., / 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
Finding Optimal Production and Selling Strategies for an Electricity Generator in a Part of a Country’s Electrical Grid
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
Методы оптимальных решений, издание 3-е, исправленное и дополненное
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
Sequence matching algorithms and paring of noncoding RNAs
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
Сравнение молекул РНК: энергия связывания и статистические свойства случайных последовательностей
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
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit