Equilibrium Models and Variational Inequalities

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

Equilibrium Models and Variational Inequalities Book 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

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: 2001
ISBN: 1402001614
Category: Computers
Language: EN, FR, DE, ES & NL

Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models Book 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.

Network Economics

Network Economics
Author: Anna Nagurney
Publsiher: Springer Science & Business Media
Total Pages: 452
Release: 1998-12-31
ISBN: 9780792383505
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Network Economics Book Excerpt:

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.

Variational Inequalities and Network Equilibrium Problems

Variational Inequalities and Network Equilibrium Problems
Author: F. Giannessi,A. Maugeri
Publsiher: Plenum Publishing Corporation
Total Pages: 330
Release: 1995-03-31
ISBN: 1928374650XXX
Category: Computers
Language: EN, FR, DE, ES & NL

Variational Inequalities and Network Equilibrium Problems Book 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 and Variational Models

Equilibrium Problems and Variational Models
Author: P. Daniele,Franco Giannessi,A. Maugeri
Publsiher: Springer Science & Business Media
Total Pages: 468
Release: 2003-06-30
ISBN: 9781402074707
Category: Mathematics
Language: EN, FR, DE, ES & NL

Equilibrium Problems and Variational Models Book 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.

Network Economics A Variational Inequality Approach

Network Economics  A Variational Inequality Approach
Author: David Ben-Arieh
Publsiher: Springer Science & Business Media
Total Pages: 326
Release: 2012-12-06
ISBN: 9401121788
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Network Economics A Variational Inequality Approach Book Excerpt:

Computational economics has been at the forefront in stimulating the de velopment of mathematical methodologies for the analysis and solution of complex, large-scale problems. The past decade, in particular, has witnessed a dramatic growth of interest in this area. Supported by the increasing avail ability of data and advances in computer architectures, the scale and scope of problems that can now be handled are unveiling new horizons in both theoretical modeling and policy analysis. Accompanying the activity in computational economics is a need for the unification, documentation, and presentation of fundamental methodologies for use by both researchers and practitioners. This volume aims to make a contribution in this direction. The focus of this book is on network economics. Physical networks are pervasive in today's society, be they in the form of transportation networks, telecommunication networks, energy pipelines, electric power networks, etc. Mathematical networks, on the other hand, may be used to represent not only physical networks but also interactions among economic agents. In many applications, the network representation of an economic equilibrium problem may be abstract in that the nodes of the network need not corre spond to locations in space and the links of the network to trade or travel routes.

Uncertainty Quantification in Variational Inequalities

Uncertainty Quantification in Variational Inequalities
Author: Joachim Gwinner,Baasansuren Jadamba,Akhtar A. Khan,Fabio Raciti
Publsiher: CRC Press
Total Pages: 404
Release: 2021-12-21
ISBN: 1351857673
Category: Mathematics
Language: EN, FR, DE, ES & NL

Uncertainty Quantification in Variational Inequalities Book Excerpt:

Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature

Vector Variational Inequalities and Vector Equilibria

Vector Variational Inequalities and Vector Equilibria
Author: F. Giannessi
Publsiher: Springer Science & Business Media
Total Pages: 544
Release: 1999-12-31
ISBN: 9780792360261
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Vector Variational Inequalities and Vector Equilibria Book Excerpt:

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.

Continuous Optimization and Variational Inequalities

Continuous Optimization and Variational Inequalities
Author: Anurag Jayswal,Tadeusz Antczak
Publsiher: CRC Press
Total Pages: 384
Release: 2022-09-13
ISBN: 1000648982
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Continuous Optimization and Variational Inequalities Book Excerpt:

The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features •The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality. •Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. •The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. •This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.

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: 146152301X
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Projected Dynamical Systems and Variational Inequalities with Applications Book 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.

Modeling Simulation and Optimization

Modeling Simulation and Optimization
Author: Shkelzen Cakaj
Publsiher: BoD – Books on Demand
Total Pages: 316
Release: 2010-04-01
ISBN: 9533070560
Category: Computers
Language: EN, FR, DE, ES & NL

Modeling Simulation and Optimization Book Excerpt:

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.

Combined Relaxation Methods for Variational Inequalities

Combined Relaxation Methods for Variational Inequalities
Author: Igor Konnov
Publsiher: Springer Science & Business Media
Total Pages: 184
Release: 2012-12-06
ISBN: 3642568866
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Combined Relaxation Methods for Variational Inequalities Book Excerpt:

Variational inequalities proved to be a very useful and powerful tool for in vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics. In fact, varia tional inequalities for example provide a unifying framework for the study of such diverse problems as boundary value problems, price equilibrium prob lems and traffic network equilibrium problems. Besides, they are closely re lated with many general problems of Nonlinear Analysis, such as fixed point, optimization and complementarity problems. As a result, the theory and so lution methods for variational inequalities have been studied extensively, and considerable advances have been made in these areas. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relax ation (CR) approach. This approach is based on combining, modifying and generalizing ideas contained in various relaxation methods. In fact, each com bined relaxation method has a two-level structure, i.e., a descent direction and a stepsize at each iteration are computed by finite relaxation procedures.

Dynamic Networks and Evolutionary Variational Inequalities

Dynamic Networks and Evolutionary Variational Inequalities
Author: Patrizia Daniele
Publsiher: Edward Elgar Publishing
Total Pages: 253
Release: 2006-01-01
ISBN: 9781781008164
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Dynamic Networks and Evolutionary Variational Inequalities Book Excerpt:

'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.

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: 1439868212
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization Book Excerpt:

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.

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: 0387242767
Category: Mathematics
Language: EN, FR, DE, ES & NL

Variational Analysis and Applications Book Excerpt:

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.

Mathematical Analysis in Interdisciplinary Research

Mathematical Analysis in Interdisciplinary Research
Author: Ioannis N. Parasidis,Efthimios Providas,Themistocles M. Rassias
Publsiher: Springer Nature
Total Pages: 1050
Release: 2021
ISBN: 3030847217
Category: Dynamics
Language: EN, FR, DE, ES & NL

Mathematical Analysis in Interdisciplinary Research Book Excerpt:

This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

Complementarity and Variational Inequalities in Electronics

Complementarity and Variational Inequalities in Electronics
Author: Daniel Goeleven
Publsiher: Academic Press
Total Pages: 208
Release: 2017-05-18
ISBN: 0128133902
Category: Mathematics
Language: EN, FR, DE, ES & NL

Complementarity and Variational Inequalities in Electronics Book Excerpt:

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

Financial Networks

Financial Networks
Author: Anna Nagurney,Stavros Siokos
Publsiher: Springer Science & Business Media
Total Pages: 494
Release: 2012-12-06
ISBN: 3642590667
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Financial Networks Book Excerpt:

Financial analysis is concerned with the study of capital flows over time and space. This book presents a new theory of multi-sector, multi-instrument financial systems based on the visualization of such systems as networks. The framework is both qualitative and computational and depends crucially on the methodologies of finite-dimensional variational inequality theory for the study of statics and equilibrium states and on projected dynamical systems for the study of dynamics and disequilibrium behavior. Moreover, it adds a graphical dimension to the fundamental economic structure of financial systems and their evolution through time.

Computational Aspects and Applications in Large Scale Networks

Computational Aspects and Applications in Large Scale Networks
Author: Valery A. Kalyagin,Panos M. Pardalos,Oleg Prokopyev,Irina Utkina
Publsiher: Springer
Total Pages: 354
Release: 2018-08-24
ISBN: 3319962477
Category: Business & Economics
Language: EN, FR, DE, ES & NL

Computational Aspects and Applications in Large Scale Networks Book Excerpt:

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.

Mathematical Models in Economics Volume II

Mathematical Models in Economics   Volume II
Author: Wei-Bin Zhang
Publsiher: EOLSS Publications
Total Pages: 542
Release: 2010-06-10
ISBN: 1848262299
Category: Economics
Language: EN, FR, DE, ES & NL

Mathematical Models in Economics Volume II Book Excerpt:

Mathematical Models in Economics is a component of Encyclopedia of Mathematical Sciences in which is part of the global Encyclopedia of Life Support Systems (EOLSS), an integrated compendium of twenty one Encyclopedias. This theme is organized into several different topics and introduces the applications of mathematics to economics. Mathematical economics has experienced rapid growth, generating many new academic fields associated with the development of mathematical theory and computer. Mathematics is the backbone of modern economics. It plays a basic role in creating ideas, constructing new theories, and empirically testing ideas and theories. Mathematics is now an integral part of economics. The main advances in modern economics are characterized by applying mathematics to various economic problems. Many of today's profound insights into economic problems could hardly be obtained without the help of mathematics. The concepts of equilibrium versus non-equilibrium, stability versus instability, and steady states versus chaos in the contemporary literature are difficult to explain without mathematics. The theme discusses on modern versions of some classical economic theories, taking account of balancing between significance of economic issues and mathematical techniques. These two volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.