April 12, 2021

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Equilibrium Models and Variational Inequalities

Equilibrium Models and Variational Inequalities
Author : Igor Konnov
Publisher : Elsevier
Release Date : 2007-02-08
Category : Mathematics
Total pages :250
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The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control. This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences. - Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field - Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models - Covers the basics of theory and solution methods both for the complementarity and variational inequality problems - The methods are illustrated by applications and exercises to economic equilibrium models

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models
Author : F. Giannessi,A. Maugeri,Panos M. Pardalos
Publisher : Springer Science & Business Media
Release Date : 2006-04-11
Category : Mathematics
Total pages :304
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The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Network Economics

Network Economics
Author : Anna Nagurney
Publisher : Springer Science & Business Media
Release Date : 2013-03-09
Category : Business & Economics
Total pages :416
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Since the publication of the first edition of Network Economics: A Variational Inequality Approach in 1993, there have been many ad vances in both methodological developments, as well as, applications in this field. These have occurred in an environment of an increasingly networked global economy, in which the importance of transportation networks and communication networks is now well-recognized, with net works such as knowledge networks, environmental networks, and finan cial networks receiving growing attention. This edition adds recent research progress in new and evolving ar eas of network economics through common and unifying principles. In addition, it includes dynamic models of traffic, of spatially separated markets, of oligopolistic markets, and of financial markets. In order to expand the range and reach of this material, we have also included a series of problems in an appendix for self-study purposes and for use in the classroom. We note that computational economics has been at the forefront in stimulating the development of mathematical methodologies for the analysis and solution of complex, large-scale problems. The past fifteen years, in particular, have witnessed a dramatic growth of interest in this area. Supported by the increasing availability of data and by advances in computer architectures, the scale and dimensions of problems that can now be handled are unveiling new horizons in both theoretical modeling and policy analysis.

Equilibrium Problems and Variational Models

Equilibrium Problems and Variational Models
Author : P. Daniele,Franco Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Release Date : 2003-06-30
Category : Mathematics
Total pages :446
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The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.

Variational Inequalities and Network Equilibrium Problems

Variational Inequalities and Network Equilibrium Problems
Author : F. Giannessi,A. Maugeri
Publisher : Springer
Release Date : 2013-06-26
Category : Social Science
Total pages :305
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This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

Finite-Dimensional Variational Inequalities and Complementarity Problems

Finite-Dimensional Variational Inequalities and Complementarity Problems
Author : Francisco Facchinei,Jong-Shi Pang
Publisher : Springer Science & Business Media
Release Date : 2007-06-04
Category : Business & Economics
Total pages :704
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This is part two of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It details algorithms for solving finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.

Projected Dynamical Systems and Variational Inequalities with Applications

Projected Dynamical Systems and Variational Inequalities with Applications
Author : Anna Nagurney,Ding Zhang
Publisher : Springer Science & Business Media
Release Date : 2012-12-06
Category : Business & Economics
Total pages :296
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Equilibrium is a concept used in operations research and economics to understand the interplay of factors and problems arising from competitive systems in the economic world. The problems in this area are large and complex and have involved a variety of mathematical methodologies. In this monograph, the authors have widened the scope of theoretical work with a new approach, `projected dynamical systems theory', to previous work in variational inequality theory. While most classical work in this area is static, the introduction to the theory of projected dynamical systems will allow many real-life dynamic situations and problems to be handled and modeled. This monograph includes: a new theoretical approach, `projected dynamical system', which allows the researcher to model real-life situations more accurately; new mathematical methods allowing researchers to combine other theoretical approaches with the projected dynamical systems approach; a framework in which research can adequately model natural, financial and human (real life) situations in competitive equilibrium problems; the computational and numerical methods for the implementation of the methods and theory discussed in the book; stability analysis, algorithms and computational procedures are offered for each set of applications.

Regional Science and Urban Economics

Regional Science and Urban Economics
Author : Anonim
Publisher : Unknown
Release Date : 1987
Category : Economics
Total pages :129
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Sample-path Solution of Stochastic Variational Inequalities and Simulation Optimization Problems

Sample-path Solution of Stochastic Variational Inequalities and Simulation Optimization Problems
Author : A. Yonca Özge
Publisher : Unknown
Release Date : 1997
Category :
Total pages :220
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Transportation Planning Models

Transportation Planning Models
Author : International Center for Transportation Studies
Publisher : Elsevier Science Limited
Release Date : 1984
Category : Business & Economics
Total pages :510
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Modelling

Modelling
Author : Stein W. Wallace
Publisher : Unknown
Release Date : 1998
Category : Computer simulation
Total pages :484
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Vector Optimization

Vector Optimization
Author : Guang-ya Chen,Xuexiang Huang,Xiaogi Yang
Publisher : Springer Science & Business Media
Release Date : 2006-03-30
Category : Business & Economics
Total pages :308
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Vector optimization model has found many important applications in decision making problems such as those in economics theory, management science, and engineering design (since the introduction of the Pareto optimal solu tion in 1896). Typical examples of vector optimization model include maxi mization/minimization of the objective pairs (time, cost), (benefit, cost), and (mean, variance) etc. Many practical equilibrium problems can be formulated as variational in equality problems, rather than optimization problems, unless further assump tions are imposed. The vector variational inequality was introduced by Gi- nessi (1980). Extensive research on its relations with vector optimization, the existence of a solution and duality theory has been pursued. The fundamental idea of the Ekeland's variational principle is to assign an optimization problem a slightly perturbed one having a unique solution which is at the same time an approximate solution of the original problem. This principle has been an important tool for nonlinear analysis and optimization theory. Along with the development of vector optimization and set-valued optimization, the vector variational principle introduced by Nemeth (1980) has been an interesting topic in the last decade. Fan Ky's minimax theorems and minimax inequalities for real-valued func tions have played a key role in optimization theory, game theory and math ematical economics. An extension was proposed to vector payoffs was intro duced by Blackwell (1955).

The Traffic Assignment Problem

The Traffic Assignment Problem
Author : Michael Patriksson
Publisher : Courier Dover Publications
Release Date : 2015-02-18
Category : Mathematics
Total pages :240
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"This unique monograph, a classic in its field, provides an account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas. The text further demonstrates the scope and limits of current models. Some familiarity with nonlinear programming theory and techniques is assumed. 1994 edition"--

Implementation and Evaluation of Network Equilibrium Models of Urban Residential Location and Travel Choices

Implementation and Evaluation of Network Equilibrium Models of Urban Residential Location and Travel Choices
Author : Chi-Kang Lee
Publisher : Unknown
Release Date : 1987
Category : Choice of transportation
Total pages :366
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Environment and Planning

Environment and Planning
Author : Anonim
Publisher : Unknown
Release Date : 2002
Category : Architecture
Total pages :129
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