Equilibrium Models and Variational Inequalities

Equilibrium Models and Variational Inequalities
Author: Igor Konnov
Publsiher: Elsevier
Total Pages: 250
Release: 2007-02-08
ISBN 10: 9780080471389
ISBN 13: 0080471382
Language: EN, FR, DE, ES & NL

Equilibrium Models and Variational Inequalities Book Review:

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
Author: F. Giannessi,A. Maugeri,Panos M. Pardalos
Publsiher: Springer Science & Business Media
Total Pages: 304
Release: 2006-04-11
ISBN 10: 0306480263
ISBN 13: 9780306480263
Language: EN, FR, DE, ES & NL

Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models Book Review:

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
Author: F. Giannessi,A. Maugeri
Publsiher: Springer Science & Business Media
Total Pages: 305
Release: 2013-06-29
ISBN 10: 1489913580
ISBN 13: 9781489913586
Language: EN, FR, DE, ES & NL

Variational Inequalities and Network Equilibrium Problems Book Review:

This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

Equilibrium Problems and Variational Models

Equilibrium Problems and Variational Models
Author: P. Daniele,F. Giannessi,A. Maugeri
Publsiher: Springer Science & Business Media
Total Pages: 446
Release: 2013-12-01
ISBN 10: 1461302390
ISBN 13: 9781461302391
Language: EN, FR, DE, ES & NL

Equilibrium Problems and Variational Models Book Review:

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.

Network Economics

Network Economics
Author: Anna Nagurney
Publsiher: Springer Science & Business Media
Total Pages: 416
Release: 2013-03-09
ISBN 10: 1475730055
ISBN 13: 9781475730050
Language: EN, FR, DE, ES & NL

Network Economics Book Review:

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.

Variational and Quasi Variational Inequalities in Mechanics

Variational and Quasi Variational Inequalities in Mechanics
Author: Alexander S. Kravchuk,Pekka J. Neittaanmäki
Publsiher: Springer Science & Business Media
Total Pages: 337
Release: 2007-09-04
ISBN 10: 1402063776
ISBN 13: 9781402063770
Language: EN, FR, DE, ES & NL

Variational and Quasi Variational Inequalities in Mechanics Book Review:

The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.

Projected Dynamical Systems and Variational Inequalities with Applications

Projected Dynamical Systems and Variational Inequalities with Applications
Author: Anna Nagurney,Ding Zhang
Publsiher: Springer Science & Business Media
Total Pages: 296
Release: 2012-12-06
ISBN 10: 146152301X
ISBN 13: 9781461523017
Language: EN, FR, DE, ES & NL

Projected Dynamical Systems and Variational Inequalities with Applications Book Review:

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.

An Introduction to Variational Inequalities and Their Applications

An Introduction to Variational Inequalities and Their Applications
Author: David Kinderlehrer,Guido Stampacchia
Publsiher: SIAM
Total Pages: 313
Release: 2000-01-01
ISBN 10: 0898714664
ISBN 13: 9780898714661
Language: EN, FR, DE, ES & NL

An Introduction to Variational Inequalities and Their Applications Book Review:

Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.

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
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
Publsiher: Unknown
Total Pages: 43
Release: 1994
ISBN 10:
ISBN 13: OCLC:32060126
Language: EN, FR, DE, ES & NL

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

Variational Analysis and Applications

Variational Analysis and Applications
Author: Franco Giannessi,Antonino Maugeri
Publsiher: Springer Science & Business Media
Total Pages: 1184
Release: 2007-03-06
ISBN 10: 0387242767
ISBN 13: 9780387242767
Language: EN, FR, DE, ES & NL

Variational Analysis and Applications Book Review:

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.

Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization

Generalized Convexity  Nonsmooth Variational Inequalities  and Nonsmooth Optimization
Author: Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Publsiher: CRC Press
Total Pages: 280
Release: 2013-07-18
ISBN 10: 1439868212
ISBN 13: 9781439868218
Language: EN, FR, DE, ES & NL

Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization Book Review:

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.

Vector Variational Inequalities and Vector Equilibria

Vector Variational Inequalities and Vector Equilibria
Author: F. Giannessi
Publsiher: Springer Science & Business Media
Total Pages: 526
Release: 2013-12-01
ISBN 10: 1461302994
ISBN 13: 9781461302995
Language: EN, FR, DE, ES & NL

Vector Variational Inequalities and Vector Equilibria Book Review:

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 Applications

Equilibrium Problems and Applications
Author: Gábor Kassay,Vicențiu Rădulescu
Publsiher: Academic Press
Total Pages: 440
Release: 2018-10-09
ISBN 10: 0128110309
ISBN 13: 9780128110300
Language: EN, FR, DE, ES & NL

Equilibrium Problems and Applications Book Review:

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

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
Author: Emre Celebi
Publsiher: Unknown
Total Pages: 108
Release: 2011
ISBN 10:
ISBN 13: OCLC:827758815
Language: EN, FR, DE, ES & NL

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

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 Optimization

Vector Variational Inequalities and Vector Optimization
Author: Qamrul Hasan Ansari,Elisabeth Köbis,Jen-Chih Yao
Publsiher: Springer
Total Pages: 509
Release: 2017-10-31
ISBN 10: 3319630490
ISBN 13: 9783319630496
Language: EN, FR, DE, ES & NL

Vector Variational Inequalities and Vector Optimization Book Review:

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.

Complementarity Applications Algorithms and Extensions

Complementarity  Applications  Algorithms and Extensions
Author: Michael C. Ferris,Olvi L. Mangasarian,Jong-Shi Pang
Publsiher: Springer Science & Business Media
Total Pages: 404
Release: 2001-02-28
ISBN 10: 9780792368168
ISBN 13: 0792368169
Language: EN, FR, DE, ES & NL

Complementarity Applications Algorithms and Extensions Book Review:

This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar kets, engineering mechanics, optimal control and asset pricing. Further more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed.

Two Theorems on Variational Inequalities for Set valued Mappings with Applications to Equilibrium Models

Two Theorems on Variational Inequalities for Set valued Mappings  with Applications to Equilibrium Models
Author: Antonio Villar
Publsiher: Unknown
Total Pages: 10
Release: 1988
ISBN 10:
ISBN 13: OCLC:46092862
Language: EN, FR, DE, ES & NL

Two Theorems on Variational Inequalities for Set valued Mappings with Applications to Equilibrium Models Book Review:

Hemivariational Inequalities

Hemivariational Inequalities
Author: Panagiotis D. Panagiotopoulos
Publsiher: Springer Science & Business Media
Total Pages: 451
Release: 2012-12-06
ISBN 10: 3642516777
ISBN 13: 9783642516771
Language: EN, FR, DE, ES & NL

Hemivariational Inequalities Book Review:

The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

The Theory of Linear Economic Models

The Theory of Linear Economic Models
Author: David Gale
Publsiher: University of Chicago Press
Total Pages: 330
Release: 1989-02-10
ISBN 10: 9780226278841
ISBN 13: 0226278840
Language: EN, FR, DE, ES & NL

The Theory of Linear Economic Models Book Review:

Reprint of the edition of 1960. Gale (math, economics, operations research, U. of Cal. Berkeley) provides a complete and systematic treatment of the topic. Annotation copyrighted by Book News, Inc., Portland, OR

Mathematical Programming and Game Theory

Mathematical Programming and Game Theory
Author: S.K. Neogy,Ravindra B. Bapat,Dipti Dubey
Publsiher: Springer
Total Pages: 226
Release: 2018-11-28
ISBN 10: 981133059X
ISBN 13: 9789811330599
Language: EN, FR, DE, ES & NL

Mathematical Programming and Game Theory Book Review:

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.