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Equilibrium Models And Variational Inequalities

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Equilibrium Models and Variational Inequalities

Equilibrium Models and Variational Inequalities Book
Author : Igor Konnov
Publisher : Elsevier
Release : 2007-02-08
ISBN : 9780080471389
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : F. Giannessi,A. Maugeri,Panos M. Pardalos
Publisher : Springer Science & Business Media
Release : 2006-04-11
ISBN : 0306480263
Language : En, Es, Fr & De

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Book Description :

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

Variational Inequalities and Network Equilibrium Problems Book
Author : F. Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 1489913580
Language : En, Es, Fr & De

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Book Description :

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

Network Economics Book
Author : Anna Nagurney
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475730055
Language : En, Es, Fr & De

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Book Description :

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.

Vector Variational Inequalities and Vector Equilibria

Vector Variational Inequalities and Vector Equilibria Book
Author : F. Giannessi
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 1461302994
Language : En, Es, Fr & De

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Book Description :

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.

Using Variational Inequalities to Solve Spatial Price Equilibrium Models with Ad Valorem Tariffs and Activity Analysis

Using Variational Inequalities to Solve Spatial Price Equilibrium Models with Ad Valorem Tariffs and Activity Analysis Book
Author : Charles F. Nicholson,Phillip M. Bishop,Anna Nagurney,New York State College of Agriculture and Life Sciences. Department of Agricultural, Resource, and Managerial Economics
Publisher : Unknown
Release : 1994
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Using Variational Inequalities to Solve Spatial Price Equilibrium Models with Ad Valorem Tariffs and Activity Analysis book written by Charles F. Nicholson,Phillip M. Bishop,Anna Nagurney,New York State College of Agriculture and Life Sciences. Department of Agricultural, Resource, and Managerial Economics, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Equilibrium Problems and Variational Models

Equilibrium Problems and Variational Models Book
Author : P. Daniele,F. Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 1461302390
Language : En, Es, Fr & De

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Book Description :

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.

Decomposition of Variational Inequalities with Applications to Nash Cournot Models in Time of Use Electricity Markets

Decomposition of Variational Inequalities with Applications to Nash Cournot Models in Time of Use Electricity Markets Book
Author : Emre Celebi
Publisher : Unknown
Release : 2011
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This thesis proposes equilibrium models to link the wholesale and retail electricity markets which allow for reconciliation of the differing time scales of responses of producers (e.g., hourly) and consumers (e.g., monthly) to changing prices. Electricity market equilibrium models with time of use (TOU) pricing scheme are formulated as large-scale variational inequality (VI) problems, a unified and concise approach for modeling the equilibrium. The demand response is dynamic in these models through a dependence on the lagged demand. Different market structures are examined within this context. With an illustrative example, the welfare gains/losses are analyzed after an implementation of TOU pricing scheme over the single pricing scheme. An approximation of the welfare change for this analysis is also presented. Moreover, break-up of a large supplier into smaller parts is investigated. For the illustrative examples presented in the dissertation, overall welfare gains for consumers and lower prices closer to the levels of perfect competition can be realized when the retail pricing scheme is changed from single pricing to TOU pricing. These models can be useful policy tools for regulatory bodies i) to forecast future retail prices (TOU or single prices), ii) to examine the market power exerted by suppliers and iii) to measure welfare gains/losses with different retail pricing schemes (e.g., single versus TOU pricing). With the inclusion of linearized DC network constraints into these models, the problem size grows considerably. Dantzig-Wolfe (DW) decomposition algorithm for VI problems is used to alleviate the computational burden and it also facilitates model management and maintenance. Modification of the DW decomposition algorithm and approximation of the DW master problem significantly improve the computational effort required to find the equilibrium. These algorithms are applied to a two-region energy model for Canada and a realistic Ontario electricity test system. In addition to empirical analysis, theoretical results for the convergence properties of the master problem approximation are presented for DW decomposition of VI problems.

Operator Theorems with Applications to Distributive Problems and Equilibrium Models

Operator Theorems with Applications to Distributive Problems and Equilibrium Models Book
Author : Antonio Villar
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3642457118
Language : En, Es, Fr & De

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Book Description :

Presentation Many economic problems, as equilibrium models, input-output analysis, rational behaviour, etc. , are usually modelled in terms of operators in Euclidean spaces. This monograph deals with the analysis of a number of formal problems involving this kind of operators (with particular reference to complementarity problems and variational inequalities), and their applications to distributive problems and equilibrium models. Thus the purpose of this work is to provide a set of new results on the solvability of those problems, and a number of economic applications that will illustrate the interest of these results in economics. It is worth stressing from the very begining that our analysis concentrates on the existence (and in some cases optimality) of solutions. That is what is meant here by solvability (in particular, nothing will be said with respect to the uniqueness, stability, sensitivity analysis or computation of solutions). The results on the solvability of operator problems presented here, were actually arrived at as a way of solving specific economic models. Yet we are going to relate this case by somehow reversing the way it happened, that is, starting with the formal results and then presenting a number of economic models which appear as applications of VIII these formal results. The rationale for this approach is twofold. First, it provides a neat track via which to go through the whole work. Then, because I would like to emphasize the interest of complementarity and variational inequalities problems in economic modelling.

Projected Dynamical Systems and Variational Inequalities with Applications

Projected Dynamical Systems and Variational Inequalities with Applications Book
Author : Anna Nagurney,Ding Zhang
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 146152301X
Language : En, Es, Fr & De

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Book Description :

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.

Equilibrium Problems and Variational Models

Equilibrium Problems and Variational Models Book
Author : P. Daniele,Franco Giannessi,A. Maugeri
Publisher : Unknown
Release : 2014-09-01
ISBN : 9781461302407
Language : En, Es, Fr & De

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Book Description :

Download Equilibrium Problems and Variational Models book written by P. Daniele,Franco Giannessi,A. Maugeri, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Quadratic Programming and Affine Variational Inequalities

Quadratic Programming and Affine Variational Inequalities Book
Author : Gue Myung Lee,N.N. Tam,Nguyen Dong Yen
Publisher : Springer Science & Business Media
Release : 2006-03-30
ISBN : 0387242783
Language : En, Es, Fr & De

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Book Description :

Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters discuss briefly two concrete nlodels (linear fractional vector optimization and the traffic equilibrium problem) whose analysis can benefit a lot from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty of a characteristic map or function is investigated, we always try first to establish necessary conditions for it to hold, then we go on to study whether the obtained necessary conditions are suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration.

Network Economics A Variational Inequality Approach

Network Economics  A Variational Inequality Approach Book
Author : David Ben-Arieh
Publisher : Springer
Release : 2012-12-24
ISBN : 9789401049641
Language : En, Es, Fr & De

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Book Description :

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.

Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models

Equilibrium Problems  Nonsmooth Optimization and Variational Inequality Models Book
Author : F. Giannessi,A. Maugeri,Panos M. Pardalos
Publisher : Springer Science & Business Media
Release : 2001
ISBN : 1402001614
Language : En, Es, Fr & De

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Book Description :

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.

On the Variational Inequality Model for Network Equilibrium

On the Variational Inequality Model for Network Equilibrium Book
Author : G. Y. Chen,N. D. Yen
Publisher : Unknown
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download On the Variational Inequality Model for Network Equilibrium book written by G. Y. Chen,N. D. Yen, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Projected Dynamical Systems and Variational Inequalities with Applications

Projected Dynamical Systems and Variational Inequalities with Applications Book
Author : Anna Nagurney,Ding Zhang
Publisher : Springer
Release : 2013-03-26
ISBN : 9781461523024
Language : En, Es, Fr & De

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Book Description :

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.

Comparative Analysis of Alternative Simultaneous Transportation Network Equilibrium Models

Comparative Analysis of Alternative Simultaneous Transportation Network Equilibrium Models Book
Author : Mohamad Kamal El-Den Ahmad Hasan
Publisher : Unknown
Release : 1991
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Comparative Analysis of Alternative Simultaneous Transportation Network Equilibrium Models book written by Mohamad Kamal El-Den Ahmad Hasan, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Essays on Variational Inequalities and Competitive Supply Chain Models

Essays on Variational Inequalities and Competitive Supply Chain Models Book
Author : Marina Zaretsky,Massachusetts Institute of Technology. Operations Research Center
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

In the first part of the thesis we combine ideas from cutting plane and interior point methods to solve variational inequality problems efficiently. In particular, we introduce "smarter" cuts into two general methods for solving these problems. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence results for both methods, as well as complexity results for one of the methods. Finally, we compare the performance of an approach that combines affine scaling and cutting plane methods with other methods for solving variational inequalities. The second part of the thesis considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multi-period environment. At each period the retailer places orders to the suppliers in response to the prices and capacities they announce. Our model allows the retailer to carry inventory. Furthermore, suppliers can expand their capacity at an additional cost; the retailer faces exogenous, price-dependent, stochastic demand. We analyze discrete as well as continuous time versions of the model: (i) we illustrate the existence of equilibrium policies; (ii) we characterize the structure of these policies; (iii) we consider coordination mechanisms; and (iv) we present some computational results. We also consider a modified model that uses option contracts and finally present some extensions.