Variational Inequalities And Network Equilibrium Problems

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Variational Inequalities and Network Equilibrium Problems

F. Giannessi,A. Maugeri
Variational Inequalities and Network Equilibrium Problems Book PDF

Author : F. Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 50,8 Mb
Release : 2013-06-29
Category : Social Science
ISBN : 9781489913586

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Variational Inequalities and Network Equilibrium Problems by F. Giannessi,A. Maugeri Pdf

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.

Network Economics

Anna Nagurney
Network Economics Book PDF

Author : Anna Nagurney
Publisher : Springer Science & Business Media
Page : 423 pages
File Size : 54,9 Mb
Release : 2013-03-09
Category : Business & Economics
ISBN : 9781475730050

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Network Economics by Anna Nagurney Pdf

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

P. Daniele,F. Giannessi,A. Maugeri
Equilibrium Problems and Variational Models Book PDF

Author : P. Daniele,F. Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 53,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302391

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Equilibrium Problems and Variational Models by P. Daniele,F. Giannessi,A. Maugeri Pdf

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.

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

F. Giannessi,A. Maugeri,Panos M. Pardalos
Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models Book PDF

Author : F. Giannessi,A. Maugeri,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 54,5 Mb
Release : 2006-04-11
Category : Mathematics
ISBN : 9780306480263

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Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models by F. Giannessi,A. Maugeri,Panos M. Pardalos Pdf

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.

Projected Dynamical Systems and Variational Inequalities with Applications

Anna Nagurney,Ding Zhang
Projected Dynamical Systems and Variational Inequalities with Applications Book PDF

Author : Anna Nagurney,Ding Zhang
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461523017

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Projected Dynamical Systems and Variational Inequalities with Applications by Anna Nagurney,Ding Zhang Pdf

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.

Vector Variational Inequalities and Vector Equilibria

F. Giannessi
Vector Variational Inequalities and Vector Equilibria Book PDF

Author : F. Giannessi
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 43,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302995

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Vector Variational Inequalities and Vector Equilibria by F. Giannessi Pdf

The book deals with the mathematical theory of vector variational inequalities with special reference to equilibrium problems. Such models have been introduced recently to study new problems from mechanics, structural engineering, networks, and industrial management, and to revisit old ones. The common feature of these problems is that given by the presence of concurrent objectives and by the difficulty of identifying a global functional (like energy) to be extremized. The vector variational inequalities have the advantage of both the variational ones and vector optimization which are found as special cases. Among several applications, the equilibrium flows on a network receive special attention. Audience: The book is addressed to academic researchers as well as industrial ones, in the fields of mathematics, engineering, mathematical programming, control theory, operations research, computer science, and economics.

Equilibrium Problems and Variational Models

P. Daniele,Franco Giannessi,A. Maugeri
Equilibrium Problems and Variational Models Book PDF

Author : P. Daniele,Franco Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 40,5 Mb
Release : 2003-06-30
Category : Mathematics
ISBN : 1402074700

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Equilibrium Problems and Variational Models by P. Daniele,Franco Giannessi,A. Maugeri Pdf

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.

Combined Relaxation Methods for Variational Inequalities

Igor Konnov
Combined Relaxation Methods for Variational Inequalities Book PDF

Author : Igor Konnov
Publisher : Springer
Page : 200 pages
File Size : 43,5 Mb
Release : 2011-04-27
Category : Electronic
ISBN : 3642568874

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Combined Relaxation Methods for Variational Inequalities by Igor Konnov Pdf

Variational inequalities proved to be a very useful tool for investigation and solution of various equilibrium type problems arising in Economics, Operations Research, Mathematical Physics, and Transportation. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relaxation approach. This approach is rather flexible and allows one to construct various methods both for single-valued and for multi-valued variational inequalities, including nonlinear constrained problems. The other essential feature of the combined relaxation methods is that they are convergent under very mild assumptions. The book can be viewed as an attempt to discribe the existing combined relaxation methods as a whole.

Dynamic Networks and Evolutionary Variational Inequalities

Patrizia Daniele
Dynamic Networks and Evolutionary Variational Inequalities Book PDF

Author : Patrizia Daniele
Publisher : Edward Elgar Publishing
Page : 280 pages
File Size : 53,7 Mb
Release : 2006-01-01
Category : Business & Economics
ISBN : 1781008167

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Dynamic Networks and Evolutionary Variational Inequalities by Patrizia Daniele Pdf

'Since the extraordinary impact of networks is self-evident today both in the field of telecommunications and transportation as well as in the field of economic and financial equilibria, the scientific work carried out by Patrizia Daniele appears as an outstanding resource. The author employs with uncommon competence mathematical topics that are at the forefront of the science, while at the same time enabling the reader to understand the matter treated without any difficulty. Moreover the reader is fascinated by the clarity, depth and soundness with which the evolutionary equilibria problems are studied and by the original efficient computational procedures which allow for the solving of many significant examples and concrete problems. Without any doubt the book represents a shining light and a necessary tool for scholars of pure and applied mathematics, for economists and engineers as well as for practitioners, general managers and managing directors.' - Antonino Maugeri, Università di Catania, Italy This book offers a comprehensive analysis of dynamic networks and evolutionary variational inequalities, a topic of growing prominence in the study of networks. The extraordinary importance of networks in finance, mathematics, computer science and other areas is well known but the relatively new concept of 'dynamic' networks is less well understood. They become dynamic when the constitutive elements of the phenomena associated with the fixed geometry of networks are considered to be evolving over time. Patrizia Daniele offers many numerical examples to illustrate the issues discussed and provides a broad appendix to enrich this challenging but deeply informative book.

Combined Relaxation Methods for Variational Inequalities

Igor Konnov
Combined Relaxation Methods for Variational Inequalities Book PDF

Author : Igor Konnov
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642568862

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Combined Relaxation Methods for Variational Inequalities by Igor Konnov Pdf

Variational inequalities proved to be a very useful and powerful tool for in vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics. In fact, varia tional inequalities for example provide a unifying framework for the study of such diverse problems as boundary value problems, price equilibrium prob lems and traffic network equilibrium problems. Besides, they are closely re lated with many general problems of Nonlinear Analysis, such as fixed point, optimization and complementarity problems. As a result, the theory and so lution methods for variational inequalities have been studied extensively, and considerable advances have been made in these areas. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relax ation (CR) approach. This approach is based on combining, modifying and generalizing ideas contained in various relaxation methods. In fact, each com bined relaxation method has a two-level structure, i.e., a descent direction and a stepsize at each iteration are computed by finite relaxation procedures.

Vector Variational Inequalities and Vector Optimization

Qamrul Hasan Ansari,Elisabeth Köbis,Jen-Chih Yao
Vector Variational Inequalities and Vector Optimization Book PDF

Author : Qamrul Hasan Ansari,Elisabeth Köbis,Jen-Chih Yao
Publisher : Springer
Page : 509 pages
File Size : 42,5 Mb
Release : 2017-10-31
Category : Business & Economics
ISBN : 9783319630496

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Vector Variational Inequalities and Vector Optimization by Qamrul Hasan Ansari,Elisabeth Köbis,Jen-Chih Yao Pdf

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Encyclopedia of Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Encyclopedia of Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 49,5 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Equilibrium Models and Variational Inequalities

Igor Konnov
Equilibrium Models and Variational Inequalities Book PDF

Author : Igor Konnov
Publisher : Elsevier
Page : 250 pages
File Size : 50,5 Mb
Release : 2007-02-08
Category : Mathematics
ISBN : 0080471382

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Equilibrium Models and Variational Inequalities by Igor Konnov Pdf

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

Network Economics: A Variational Inequality Approach

David Ben-Arieh
Network Economics A Variational Inequality Approach Book PDF

Author : David Ben-Arieh
Publisher : Springer
Page : 326 pages
File Size : 43,8 Mb
Release : 2012-12-24
Category : Business & Economics
ISBN : 9401049645

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Network Economics: A Variational Inequality Approach by David Ben-Arieh Pdf

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.

Financial Networks

Anna Nagurney,Stavros Siokos
Financial Networks Book PDF

Author : Anna Nagurney,Stavros Siokos
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642590665

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Financial Networks by Anna Nagurney,Stavros Siokos Pdf

Financial analysis is concerned with the study of capital flows over time and space. This book presents a new theory of multi-sector, multi-instrument financial systems based on the visualization of such systems as networks. The framework is both qualitative and computational and depends crucially on the methodologies of finite-dimensional variational inequality theory for the study of statics and equilibrium states and on projected dynamical systems for the study of dynamics and disequilibrium behavior. Moreover, it adds a graphical dimension to the fundamental economic structure of financial systems and their evolution through time.