Equilibrium Models and Variational Inequalities Book

Equilibrium Models and Variational Inequalities


  • Author : Igor Konnov
  • Publisher : Elsevier
  • Release Date : 2007-02-08
  • Genre: Mathematics
  • Pages : 250
  • ISBN 10 : 0080471382

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Equilibrium Models and Variational Inequalities Excerpt :

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 Book

Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models


  • Author : F. Giannessi
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-04-11
  • Genre: Mathematics
  • Pages : 304
  • ISBN 10 : 9780306480263

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Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models Excerpt :

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.

Variational Inequalities and Network Equilibrium Problems Book

Variational Inequalities and Network Equilibrium Problems


  • Author : F. Giannessi
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Social Science
  • Pages : 305
  • ISBN 10 : 9781489913586

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Variational Inequalities and Network Equilibrium Problems Excerpt :

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.

Equilibrium Problems and Variational Models Book

Equilibrium Problems and Variational Models


  • Author : P. Daniele
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-12-01
  • Genre: Mathematics
  • Pages : 446
  • ISBN 10 : 9781461302391

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Equilibrium Problems and Variational Models Excerpt :

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.

Network Economics Book

Network Economics


  • Author : Anna Nagurney
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Business & Economics
  • Pages : 416
  • ISBN 10 : 9781475730050

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Network Economics Excerpt :

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 Applications Book

Equilibrium Problems and Applications


  • Author : Gábor Kassay
  • Publisher : Academic Press
  • Release Date : 2018-10-09
  • Genre: Business & Economics
  • Pages : 440
  • ISBN 10 : 9780128110300

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Equilibrium Problems and Applications Excerpt :

Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn

Uncertainty Quantification in Variational Inequalities Book

Uncertainty Quantification in Variational Inequalities


  • Author : Joachim Gwinner
  • Publisher : CRC Press
  • Release Date : 2021-12-21
  • Genre: Mathematics
  • Pages : 404
  • ISBN 10 : 9781351857666

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Uncertainty Quantification in Variational Inequalities Excerpt :

Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature

Network Economics Book
Score: 4
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Network Economics


  • Author : Anna Nagurney
  • Publisher : Springer Science & Business Media
  • Release Date : 1998-12-31
  • Genre: Business & Economics
  • Pages : 452
  • ISBN 10 : 0792383508

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Network Economics Excerpt :

The second and revised edition of Network Economics: A Variational Inequality Approach provides an updated treatment of network economics through the inclusion of new theoretical results and new applications, as well as problems for self-study purposes and/or for use in the classroom. This volume remains true to the first edition in that it provides a unified treatment of finite-dimensional variational inequalities, algorithms, and applications. Physical networks are pervasive in today's society in the form of transportation networks, telecommunication networks, energy networks, and financial networks, whereas mathematical networks provide a mechanism for studying a plethora of economic equilibrium problems through a common graphic structure. Network Economics establishes the connections among economic equilibrium problems through their network structure and demonstrates how the structure can then be used to address policy interventions, as well as to construct efficient numerical schemes for the computation of equilibria. The network framework provides not only a mechanism for the graphic representation of economic problems and a means for visualizing their similarities and differences, but, in addition, a novel theoretical approach. Problems treated include: congested transportation systems, oligopolistic market equilibrium problems, problems of human migration, and general financial and economic equilibrium problems. New applications covered in this second edition include environmental networks and knowledge networks.

Network Economics  A Variational Inequality Approach Book

Network Economics A Variational Inequality Approach


  • Author : David Ben-Arieh
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Business & Economics
  • Pages : 326
  • ISBN 10 : 9789401121781

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Network Economics A Variational Inequality Approach Excerpt :

Computational economics has been at the forefront in stimulating the de velopment of mathematical methodologies for the analysis and solution of complex, large-scale problems. The past decade, in particular, has witnessed a dramatic growth of interest in this area. Supported by the increasing avail ability of data and advances in computer architectures, the scale and scope of problems that can now be handled are unveiling new horizons in both theoretical modeling and policy analysis. Accompanying the activity in computational economics is a need for the unification, documentation, and presentation of fundamental methodologies for use by both researchers and practitioners. This volume aims to make a contribution in this direction. The focus of this book is on network economics. Physical networks are pervasive in today's society, be they in the form of transportation networks, telecommunication networks, energy pipelines, electric power networks, etc. Mathematical networks, on the other hand, may be used to represent not only physical networks but also interactions among economic agents. In many applications, the network representation of an economic equilibrium problem may be abstract in that the nodes of the network need not corre spond to locations in space and the links of the network to trade or travel routes.

Uncertainty Quantification in Variational Inequalities Book

Uncertainty Quantification in Variational Inequalities


  • Author : Joachim Gwinner
  • Publisher : CRC Press
  • Release Date : 2021-12-21
  • Genre: Mathematics
  • Pages : 404
  • ISBN 10 : 9781351857673

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Uncertainty Quantification in Variational Inequalities Excerpt :

Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature

Projected Dynamical Systems and Variational Inequalities with Applications Book

Projected Dynamical Systems and Variational Inequalities with Applications


  • Author : Anna Nagurney
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Business & Economics
  • Pages : 296
  • ISBN 10 : 9781461523017

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Projected Dynamical Systems and Variational Inequalities with Applications Excerpt :

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.

Finite Dimensional Variational Inequalities and Complementarity Problems Book

Finite Dimensional Variational Inequalities and Complementarity Problems


  • Author : Francisco Facchinei
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-06-14
  • Genre: Mathematics
  • Pages : 693
  • ISBN 10 : 9780387218144

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Finite Dimensional Variational Inequalities and Complementarity Problems Excerpt :

This is part one of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It covers the basic theory of 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.

Continuous Optimization and Variational Inequalities Book

Continuous Optimization and Variational Inequalities


  • Author : Anurag Jayswal
  • Publisher : CRC Press
  • Release Date : 2022-09-13
  • Genre: Technology & Engineering
  • Pages : 384
  • ISBN 10 : 9781000648980

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Continuous Optimization and Variational Inequalities Excerpt :

The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features •The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality. •Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. •The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. •This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.