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

Equilibrium Problems and Applications Excerpt :

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

Equilibrium Problems and Variational Models Book

Equilibrium Problems and Variational Models

  • Author : P. Daniele
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-12-01
  • Genre: Mathematics
  • Pages : 446
  • ISBN 10 : 9781461302391

Equilibrium Problems and Variational Models Excerpt :

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.

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

Variational Inequalities and Network Equilibrium Problems Excerpt :

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  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

Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models Excerpt :

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.

Generalized Nash Equilibrium Problems  Bilevel Programming and MPEC Book

Generalized Nash Equilibrium Problems Bilevel Programming and MPEC

  • Author : Didier Aussel
  • Publisher : Springer
  • Release Date : 2018-04-03
  • Genre: Mathematics
  • Pages : 124
  • ISBN 10 : 9789811047749

Generalized Nash Equilibrium Problems Bilevel Programming and MPEC Excerpt :

The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.

Complementarity  Equilibrium  Efficiency and Economics Book
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Complementarity Equilibrium Efficiency and Economics

  • Author : G. Isac
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-17
  • Genre: Mathematics
  • Pages : 449
  • ISBN 10 : 9781475736236

Complementarity Equilibrium Efficiency and Economics Excerpt :

In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

Equilibrium and Advanced Transportation Modelling Book

Equilibrium and Advanced Transportation Modelling

  • Author : P. Marcotte
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Business & Economics
  • Pages : 325
  • ISBN 10 : 9781461557579

Equilibrium and Advanced Transportation Modelling Excerpt :

Each chapter in Equilibrium and Advanced Transportation Modelling develops a topic from basic concepts to the state-of-the-art, and beyond. All chapters relate to aspects of network equilibrium. Chapter One advocates the use of simulation models for the representation of traffic flow movements at the microscopic level. Chapter Two presents travel demand systems for generating trip matrices from activity-based models, taking into account the entire daily schedule of network users. Chapter Three examines equilibrium strategic choices adopted by the passengers of a congested transit system, carefully addressing line selection at boarding and transfer nodes. Chapter Four provides a critical appraisal of the traditional process that consists in sequentially performing the tasks of trip generation, trip distribution, mode split and assignment, and its impact on the practice of transportation planning. Chapter Five gives an insightful overview of stochastic assignment models, both in the static and dynamic cases. Chapters Six and Seven investigate the setting of tolls to improve traffic flow conditions in a congested transportation network. Chapter Eight provides a unifying framework for the analysis of multicriteria assignment models. In this chapter, available algorithms are summarized and an econometric perspective on the estimation of heterogeneous preferences is given. Chapter Nine surveys the use of hyperpaths in operations research and proposes a new paradigm of equilibrium in a capacitated network, with an application to transit assignment. Chapter Ten analyzes the transient states of a system moving towards equilibrium, using the mathematical framework of projected dynamical systems. Chapter Eleven discusses an in-depth survey of algorithms for solving shortest path problems, which are pervasive to any equilibrium algorithm. The chapter devotes special attention to the computation of dynamic shortest paths and to shortest hyperpaths. The final chapter considers op

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

Projected Dynamical Systems and Variational Inequalities with Applications Excerpt :

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.

Forefronts Book


  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 1985
  • Genre: Computer simulation
  • Pages : 586
  • ISBN 10 : CORNELL:31924004397992

Forefronts Excerpt :

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

Equilibrium Models and Variational Inequalities Excerpt :

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

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints Book

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints

  • Author : Jiri Outrata
  • Publisher : Springer Science & Business Media
  • Release Date : 1998-07-31
  • Genre: Business & Economics
  • Pages : 300
  • ISBN 10 : 9780792351702

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints Excerpt :

This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints: parameter-dependent convex programs, variational inequalities or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools: a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method. This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization will also find the book useful.

Recent Developments in Sustainable Infrastructure Book

Recent Developments in Sustainable Infrastructure

  • Author : Bibhuti Bhusan Das
  • Publisher : Springer Nature
  • Release Date : 2020-07-03
  • Genre: Technology & Engineering
  • Pages : 1106
  • ISBN 10 : 9789811545771

Recent Developments in Sustainable Infrastructure Excerpt :

This book comprises select peer-reviewed proceedings of the International Conference on Recent Developments in Sustainable Infrastructure (ICRDSI) 2019. The topics span over all major disciplines of civil engineering with regard to sustainable development of infrastructure and innovation in construction materials, especially concrete. The book covers numerical and analytical studies on various topics such as composite and sandwiched structures, green building, groundwater modeling, rainwater harvesting, soil dynamics, seismic resistance and control of structures, waste management, structural health monitoring, and geo-environmental engineering. This book will be useful for students, researchers and professionals working in sustainable technologies in civil engineering.