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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.

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.

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.

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.

Network Economics

Network Economics Book
Author : Anna Nagurney
Publisher : Springer Science & Business Media
Release : 1998-12-31
ISBN : 9780792383505
Language : En, Es, Fr & De

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Book Description :

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.

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.

Modeling Simulation and Optimization

Modeling Simulation and Optimization Book
Author : Shkelzen Cakaj
Publisher : BoD – Books on Demand
Release : 2010-04-01
ISBN : 9533070560
Language : En, Es, Fr & De

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Book Description :

Parametric representation of shapes, mechanical components modeling with 3D visualization techniques using object oriented programming, the well known golden ratio application on vertical and horizontal displacement investigations of the ground surface, spatial modeling and simulating of dynamic continuous fluid flow process, simulation model for waste-water treatment, an interaction of tilt and illumination conditions at flight simulation and errors in taxiing performance, plant layout optimal plot plan, atmospheric modeling for weather prediction, a stochastic search method that explores the solutions for hill climbing process, cellular automata simulations, thyristor switching characteristics simulation, and simulation framework toward bandwidth quantization and measurement, are all topics with appropriate results from different research backgrounds focused on tolerance analysis and optimal control provided in this book.

Variational Analysis and Applications

Variational Analysis and Applications Book
Author : Franco Giannessi,Antonino Maugeri
Publisher : Springer Science & Business Media
Release : 2007-03-06
ISBN : 0387242767
Language : En, Es, Fr & De

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Book Description :

This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.

Dynamic Networks and Evolutionary Variational Inequalities

Dynamic Networks and Evolutionary Variational Inequalities Book
Author : Patrizia Daniele
Publisher : Edward Elgar Publishing
Release : 2006-01-01
ISBN : 9781781008164
Language : En, Es, Fr & De

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Book Description :

'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.

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.

Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization

Generalized Convexity  Nonsmooth Variational Inequalities  and Nonsmooth Optimization Book
Author : Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Publisher : CRC Press
Release : 2013-07-18
ISBN : 1439868212
Language : En, Es, Fr & De

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Book Description :

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction. The first part of the book focuses on generalized convexity and generalized monotonicity. The authors investigate convexity and generalized convexity for both the differentiable and nondifferentiable case. For the nondifferentiable case, they introduce the concepts in terms of a bifunction and the Clarke subdifferential. The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings. The book discusses existence and uniqueness criteria for a variational inequality, the gap function associated with it, and numerical methods to solve it. It also examines characterizations of a solution set of an optimization problem and explores variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential. Integrating results on convexity, monotonicity, and variational inequalities into one unified source, this book deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The book shows how variational inequality theory not only serves as a tool for formulating a variety of equilibrium problems, but also provides algorithms for computational purposes.

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.

Equilibrium Facility Location on Networks

Equilibrium Facility Location on Networks Book
Author : Tan C. Miller,Terry L. Friesz,Roger L. Tobin
Publisher : Springer Science & Business Media
Release : 2013-04-18
ISBN : 3662032805
Language : En, Es, Fr & De

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Book Description :

This is a book about the simultaneous location, production and distri bution decisions of a firm entering a competitive market whose spatial nature is describable by a network in which the market either achieves an equilibrium or is equilibrium tending. As such, the problem is of clear theoretical and practical importance, for it is a rather general version of the problem faced by real firms every day in deciding where to locate. Further, the timeliness of this subject manifests itself in the growing excitement and interest found both in the research/academic communities and in the practitioner/private industry communities for more comprehensive approaches to competitive facility location analy sis and equilibrium modeling of networks. The desire both for new conceptual approaches yielding enhanced insights and for practical methodologies to capture these insights drives this interest. While nor mative, deterministic facility location modeling techniques currently provide valuable input into the location decision-making process, re searchers and practitioners alike have realized the vast and relatively untapped potential of more advanced location decision making tech niques. In this book, we develop what we believe represents a major new line of research in the field of competitive facility location analysis; namely, equilibrium facility location modeling. In particular, this book offers a number of innovations in the mathe matical analysis and computation of solutions to location models which we have pioneered and which are collected under a single cover for the first time.

Complementarity and Variational Inequalities in Electronics

Complementarity and Variational Inequalities in Electronics Book
Author : Daniel Goeleven
Publisher : Academic Press
Release : 2017-05-18
ISBN : 0128133902
Language : En, Es, Fr & De

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Book Description :

Complementarity and Variational Inequalities in Electronics evaluates the main mathematical models relevant to the study of electrical network problems involving devices. The book focuses on complementarity problems, variational inequalities and non-regular dynamical systems which are well-known for their applications in mechanics and economics, but rarely target electrical applications. The book uses these tools to review the qualitative properties of devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers. Users will find demonstrations on how to compute optimized output signal relevant to potentially superior applications. In addition, the book describes how to determine the stationary points of dynamical circuits and to determine the corresponding Lyapunov stability and attractivity properties, topics of major importance for further dynamical analysis and control. Hemivariational inequalities are also covered in some depth relevant to application in thyristor devices. Reviews the main mathematical models applicable to the study of electrical networks involving diodes and transistors Focuses on theoretical existence and uniqueness of a solution, stability of stationary solutions, and invariance properties Provides realistic complementarity and variational problems to illustrate theoretical results Evaluates applications of the theory across many devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers Details both fully developed mathematical proofs and common models used in electronics Provides a comprehensive literature review, including thousands of relevant references

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.

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.

Computational Aspects and Applications in Large Scale Networks

Computational Aspects and Applications in Large Scale Networks Book
Author : Valery A. Kalyagin,Panos M. Pardalos,Oleg Prokopyev,Irina Utkina
Publisher : Springer
Release : 2018-08-24
ISBN : 3319962477
Language : En, Es, Fr & De

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Book Description :

Contributions in this volume focus on computationally efficient algorithms and rigorous mathematical theories for analyzing large-scale networks. Researchers and students in mathematics, economics, statistics, computer science and engineering will find this collection a valuable resource filled with the latest research in network analysis. Computational aspects and applications of large-scale networks in market models, neural networks, social networks, power transmission grids, maximum clique problem, telecommunication networks, and complexity graphs are included with new tools for efficient network analysis of large-scale networks. This proceeding is a result of the 7th International Conference in Network Analysis, held at the Higher School of Economics, Nizhny Novgorod in June 2017. The conference brought together scientists, engineers, and researchers from academia, industry, and government.