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

GET BOOK
Equilibrium Models and Variational Inequalities 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 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

GET BOOK
Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models 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 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

GET BOOK
Variational Inequalities and Network Equilibrium Problems 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 Book

Network Economics


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

GET BOOK
Network Economics 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 Book

Vector Variational Inequalities and Vector Equilibria


  • Author : F. Giannessi
  • Publisher : Springer Science & Business Media
  • Release Date : 1999-12-31
  • Genre: Business & Economics
  • Pages : 523
  • ISBN 10 : 0792360265

GET BOOK
Vector Variational Inequalities and Vector Equilibria 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.

Equilibrium Problems and Variational Models Book

Equilibrium Problems and Variational Models


  • Author : P. Daniele
  • Publisher : Springer Science & Business Media
  • Release Date : 2003-06-30
  • Genre: Mathematics
  • Pages : 446
  • ISBN 10 : 1402074700

GET BOOK
Equilibrium Problems and Variational Models 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.

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 : 2007-06-04
  • Genre: Business & Economics
  • Pages : 704
  • ISBN 10 : 9780387218151

GET BOOK
Finite Dimensional Variational Inequalities and Complementarity Problems Book Description :

This is part two of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It details algorithms for solving finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.

Projected Dynamical Systems and Variational Inequalities with Applications 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

GET BOOK
Projected Dynamical Systems and Variational Inequalities with Applications 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 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

GET BOOK
Equilibrium Problems and Applications Book Description :

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

Vector Variational Inequalities and Vector Optimization Book

Vector Variational Inequalities and Vector Optimization


  • Author : Qamrul Hasan Ansari
  • Publisher : Springer
  • Release Date : 2017-10-31
  • Genre: Business & Economics
  • Pages : 509
  • ISBN 10 : 9783319630496

GET BOOK
Vector Variational Inequalities and Vector Optimization Book Description :

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.

Mathematical Programming and Game Theory Book

Mathematical Programming and Game Theory


  • Author : S.K. Neogy
  • Publisher : Springer
  • Release Date : 2018-11-28
  • Genre: Mathematics
  • Pages : 226
  • ISBN 10 : 9789811330599

GET BOOK
Mathematical Programming and Game Theory Book Description :

This book discusses recent developments in mathematical programming and game theory, and the application of several mathematical models to problems in finance, games, economics and graph theory. All contributing authors are eminent researchers in their respective fields, from across the world. This book contains a collection of selected papers presented at the 2017 Symposium on Mathematical Programming and Game Theory at New Delhi during 9–11 January 2017. Researchers, professionals and graduate students will find the book an essential resource for current work in mathematical programming, game theory and their applications in finance, economics and graph theory. The symposium provides a forum for new developments and applications of mathematical programming and game theory as well as an excellent opportunity to disseminate the latest major achievements and to explore new directions and perspectives.

Dynamic Networks and Evolutionary Variational Inequalities Book

Dynamic Networks and Evolutionary Variational Inequalities


  • Author : Patrizia Daniele
  • Publisher : Edward Elgar Publishing
  • Release Date : 2006-01-01
  • Genre: Business & Economics
  • Pages : 253
  • ISBN 10 : 1781008167

GET BOOK
Dynamic Networks and Evolutionary Variational Inequalities 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.

Operator Theorems with Applications to Distributive Problems and Equilibrium Models Book

Operator Theorems with Applications to Distributive Problems and Equilibrium Models


  • Author : Antonio Villar
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Business & Economics
  • Pages : 160
  • ISBN 10 : 9783642457111

GET BOOK
Operator Theorems with Applications to Distributive Problems and Equilibrium Models 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.

Generalized Convexity  Generalized Monotonicity  Recent Results Book

Generalized Convexity Generalized Monotonicity Recent Results


  • Author : Jean-Pierre Crouzeix
  • Publisher : Springer Science & Business Media
  • Release Date : 1998-08-31
  • Genre: Mathematics
  • Pages : 471
  • ISBN 10 : 079235088X

GET BOOK
Generalized Convexity Generalized Monotonicity Recent Results Book Description :

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems.

Quadratic Programming and Affine Variational Inequalities Book

Quadratic Programming and Affine Variational Inequalities


  • Author : Gue Myung Lee
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-03-30
  • Genre: Mathematics
  • Pages : 346
  • ISBN 10 : 9780387242781

GET BOOK
Quadratic Programming and Affine Variational Inequalities 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.