Equilibrium models and variational inequalities / I.V. Konnov.

Format:

Book

Author/Creator:

Konnov, Igor, 1958-

Series:

Mathematics in science and engineering ; v. 210.

Mathematics in science and engineering, 0076-5392 ; v. 210

Language:

English

Subjects (All):

Variational inequalities (Mathematics).

Equilibrium (Economics).

Physical Description:

1 online resource (251 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam ; Boston : Elsevier, 2007.

Language Note:

English

Summary:

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 r

Contents:

Front Cover; Equilibrium Models and Variational Inequalities; Copyright Page; Preface; Table of Contents; List of Figures; Chapter 1 Introduction; Part I MODELS; Chapter 2 Linear Models in Economics; 2.1 Open input-output model; 2.2 Generalizations; 2.3 Closed input-output model; Chapter 3 Linear Dynamic Models of an Economy; 3.1 Extended dynamic input-output model; 3.2 The von Neumann model of an expanding economy; Chapter 4 Optimization and Equilibria; 4.1 Linear programming problems; 4.2 Economic interpretation of optimality conditions; 4.3 Economic interpretation of the solution method

Chapter 5 Nonlinear Economic Equilibrium Models5.1 Cassel-Wald type economic equilibrium models; 5.2 General price equilibrium models; 5.3 Spatial price equilibrium models; 5.4 Imperfectly competitive equilibrium models; Chapter 6 Transportation and Migration Models; 6.1 Network equilibrium models; 6.2 Migration equilibrium models; Part II COMPLEMENTARITY PROBLEMS; Chapter 7 Complementarity with Z Properties; 7.1 Classes of complementarity problems; 7.2 Classes of square matrices and their properties; 7.3 Complementarity problems with Z cost mappings; Chapter 8 Applications

8.1 Input-output models8.2 Price equilibrium models; 8.3 A pure trade market model; 8.4 Price oligopoly models; Chapter 9 Complementarity with P Properties; 9.1 Existence and uniqueness results; 9.2 Solution methods for CP's with P properties; Chapter 10 Applications; 10.1 Walrasian price equilibrium models; 10.2 Oligopolistic equilibrium models; Part III VARIATIONAL INEQUALITIES; Chapter 11 Theory of Variational Inequalities; 11.1 Variational inequalities and related problems; 11.2 Existence and uniqueness results; Chapter 12 Applications; 12.1 Cassel-Wald equilibrium models

12.2 Walrasian equilibrium models and their modifications12.3 Existence results in Walrasian equilibrium models; 12.4 Imperfect competition models; 12.5 Network and migration equilibrium models; Chapter 13 Projection Type Methods; 13.1 The classical projection method; 13.2 The projection methods with linesearch; 13.3 Modifications and extensions; Chapter 14 Applications of the Projection Methods; 14.1 Applications to variational inequalities; 14.2 Applications to systems of variational inequalities; Chapter 15 Regularization Methods

15.1 The classical regularization method and its modifications15.2 The proximal point method; Chapter 16 Direct Iterative Methods for Monotone Variational Inequalities; 16.1 Extrapolation methods; 16.2 The ellipsoid method; Chapter 17 Solutions to Exercises; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-280-96260-7

9786610962600

0-08-047138-2

OCLC:

476040860