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Search Results: 1 - 10 of 117819 matches for " T Terlaky "
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An efficient optimisation method in groundwater resource management
JM Ndambuki, FAO Otieno, CBM Stroet, T Terlaky, EJM Veling
Water SA , 2003,
Abstract: Uncertainty in input parameters to groundwater flow problems has been recognised as an impediment to designing efficient groundwater management strategies. The most popular approach to tackling this problem has been through the Monte Carlo approach. However, this approach is generally too expensive in terms of computer time because of the number of scenarios required to ensure reliable statistics. Furthermore, solutions obtained through this approach are not necessarily robust. In this paper, it is shown how groundwater management problems, where input parameters are uncertain can be reformulated as second-order cone optimisation (SOCO) problems, which are efficiently solved by recently developed interior-point methods. Results for a real-world case application of a groundwater aquifer found in Kenya are presented. Water SA Vol.29(4): 359-363
A Multilevel Congestion-Based Global Router
Logan Rakai,Laleh Behjat,Shawki Areibi,Tamas Terlaky
VLSI Design , 2009, DOI: 10.1155/2009/537341
Abstract: Routing in nanometer nodes creates an elevated level of importance for low-congestion routing. At the same time, advances in mathematical programming have increased the power to solve complex problems, such as the routing problem. Hence, new routing methods need to be developed that can combine advanced mathematical programming and modeling techniques to provide low-congestion solutions. In this paper, a hierarchical mathematical programming-based global routing technique that considers congestion is proposed. The main contributions presented in this paper include (i) implementation of congestion estimation based on actual routing solutions versus purely probabilistic techniques, (ii) development of a congestion-based hierarchy for solving the global routing problem, and (iii) generation of a robust framework for solving the routing problem using mathematical programming techniques. Experimental results illustrate that the proposed global router is capable of reducing congestion and overflow by as much as 36% compared to the state-of-the-art mathematical programming models.
The Colourful Feasibility Problem
Antoine Deza,Sui Huang,Tamon Stephen,Tamás Terlaky
Mathematics , 2005,
Abstract: We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Barany and Onn with new methods. We perform benchmarking on generic and ill-conditioned problems, as well as as recently introduced highly structured problems. We show that some algorithms can lead to cycling or slow convergence, but we provide extensive numerical experiments which show that others perform much better than predicted by complexity arguments. We conclude that the most efficient method for all but the most ill-conditioned problems is a proposed multi-update algorithm.
Colourful Simplicial Depth
Antoine Deza,Sui Huang,Tamon Stephen,Tamás Terlaky
Mathematics , 2005,
Abstract: Inspired by Barany's colourful Caratheodory theorem, we introduce a colourful generalization of Liu's simplicial depth. We prove a parity property and conjecture that the minimum colourful simplicial depth of any core point in any d-dimensional configuration is d^2+1 and that the maximum is d^(d+1)+1. We exhibit configurations attaining each of these depths and apply our results to the problem of bounding monochrome (non-colourful) simplicial depth.
Steplength Thresholds for Invariance Preserving of Discretization Methods of Dynamical Systems on a Polyhedron
Zoltán Horváth,Yunfei Song,and Tamás Terlaky
Mathematics , 2014,
Abstract: Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first positive zeros of a finite number of polynomial functions. Further, a simple and efficient algorithm is proposed to numerically compute the steplength threshold. For rational function type discretization methods we derive a valid steplength threshold for invariance preserving, which can be computed by using an analogous algorithm as in the first case. The relationship between the previous two types of discretization methods and the forward Euler method is studied. Finally, we show that, for the forward Euler method, the largest steplength threshold for invariance preserving can be computed by solving a finite number of linear optimization problems.
A Novel Unified Approach to Invariance in Control
Zoltán Horváth,Yunfei Song,Tamás Terlaky
Mathematics , 2014,
Abstract: In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear continuous or discrete dynamical system. In proving invariance of ellipsoids and Lorenz cones for discrete systems, instead of the traditional Lyapunov method, our novel proofs are based on the S-lemma, which enables us to extend invariance conditions to any set represented by a quadratic inequality. Such sets include nonconvex and unbounded sets. Finally, according to the framework of our novel method, sufficient and necessary conditions for continuous systems are derived from the sufficient and necessary conditions for the corresponding discrete systems that are obtained by Euler methods.
REGULARYFRAMWORK AND LEGAL BASE OF ELECTRONIC DOCUMENT CIRCULATION НОРМАТИВНО-ПРАВОВА БАЗА ЕЛЕКТРОННОГО ДОКУМЕНТООБ ГУ
T.Г. Омельченко,Н.А. Джанджгава
Information Technologies and Learning Tools , 2010,
Abstract: The general characteristic of legal base of electronic document circulation is presented in the article. It legislatively regulates the relations which connected with the information and information communication technologies. There is presented the list of the basic acts of regulation of sphere of information relations. У робот подано загальну характеристику нормативно-правово бази, яка законодавчо регулю в дносини, пов'язан з нформац ю, нформац йно-комун кац йними технолог ями, представлено перел к основних законодавчих акт в регулювання сфери нформац йних в дносин.
THE APPROACH OF COMPETENCE AT THE STUDY OF MATHEMATICAL INFORMATICS IN A PEDAGOGICAL UNIVERSITY КОМПЕТЕНТН СНИЙ П ДХ Д ПРИ ВИВЧЕНН МАТЕМАТИЧНО НФОРМАТИКИ” У ПЕДАГОГ ЧНОМУ УН ВЕРСИТЕТ
T.П. Кобильник
Information Technologies and Learning Tools , 2010,
Abstract: In the paper the approach of competence at the study of mathematical informatics in a pedagogical university is considered. The special attention is paid to forming of professional pedagogical and educational-cognitive competences. The example of tasks on which formed a competence at the study of mathematical informatics is resulted. У статт розглянуто компетентн сний п дх д при вивченн математично нформатики у педагог чному ун верситет . Особливу увагу звернено на формування профес йно педагог чно та навчально-п знавальну компетентност . Наведено приклад завдань, як сприяють формуванню компетентностей при вивченн математично нформатики.
SYSTEM OF THE AUTOMATIC DOCUMENT PROCESSING IN SHELL OF BASE SOFTWARE СИСТЕМА АВТОМАТИЗОВАНОГО ДОКУМЕНТООБ ГУ В ОБОЛОНЦ БАЗОВОГО ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ
В.Ю. Биков,T.О. Дерба
Information Technologies and Learning Tools , 2010,
Abstract: In the article the automatic system of the document processing, created with use of Microsoft Access – a component part of Microsoft Office is offered. This system can be used at school and Institutions of education with one computer or with system of 15 ones connecting in the local net. У статт запропоновано для ознайомлення автоматизовану систему документооб гу, створену з використанням Microsoft Access – складово частини Microsoft Office. Ця система може використовуватися в школах установах осв тньо галуз на одному комп’ютер чи на систем до 15 комп’ютер в, пов’язаних локальною мережею.
MODERN APPROACHES AND PRINCIPLES OF PORTAL BUILDING ТЕХНОЛОГ ЧН ОСНОВИ СТВОРЕННЯ ТА П ДТРИМКИ ПОРТАЛ В
Н.Т. Задорожна,T.Г. Омельченко
Information Technologies and Learning Tools , 2010,
Abstract: The paper presents the analysis of modern state of development and use of Internet portals, the peculiarities of approaches to creation and introduction of portals in educational system are described. В робот анал зуються принципи розробки та використання нтернет-портал в, описуються особливост п дход в до створення та впровадження портал в у систему осв ти.
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