Variational Methods in Economics

Variational Methods in Economics PDF Author: G. Hadley
Publisher: Elsevier
ISBN: 1483275280
Category : Business & Economics
Languages : en
Pages : 389

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Book Description
Advanced Textbooks in Economics, Volume 1: Variational Methods in Economics focuses on the application of variational methods in economics, including autonomous system, dynamic programming, and phase spaces and diagrams. The manuscript first elaborates on growth models in economics and calculus of variations. Discussions focus on connection with dynamic programming, variable end points-free boundaries, transversality at infinity, sensitivity analysis-end point changes, Weierstrass and Legendre necessary conditions, and phase diagrams and phase spaces. The text then ponders on the constraints of classical theory, including unbounded intervals of integration, free boundary conditions, comparison functions, normality, and the problem of Bolza. The publication explains two-sector models of optimal economic growth, optimal control theory, and connections with the classical theory. Topics include capital good immobile between industries, constrained state variables, linear control problems, conversion of a control problem into a problem of Lagrange, and the conversion of a nonautonomous system into an autonomous system. The book is a valuable source of information for economists and researchers interested in the variational methods in economics.

Variational Methods in Economics

Variational Methods in Economics PDF Author: G. Hadley
Publisher: Elsevier
ISBN: 1483275280
Category : Business & Economics
Languages : en
Pages : 389

Get Book Here

Book Description
Advanced Textbooks in Economics, Volume 1: Variational Methods in Economics focuses on the application of variational methods in economics, including autonomous system, dynamic programming, and phase spaces and diagrams. The manuscript first elaborates on growth models in economics and calculus of variations. Discussions focus on connection with dynamic programming, variable end points-free boundaries, transversality at infinity, sensitivity analysis-end point changes, Weierstrass and Legendre necessary conditions, and phase diagrams and phase spaces. The text then ponders on the constraints of classical theory, including unbounded intervals of integration, free boundary conditions, comparison functions, normality, and the problem of Bolza. The publication explains two-sector models of optimal economic growth, optimal control theory, and connections with the classical theory. Topics include capital good immobile between industries, constrained state variables, linear control problems, conversion of a control problem into a problem of Lagrange, and the conversion of a nonautonomous system into an autonomous system. The book is a valuable source of information for economists and researchers interested in the variational methods in economics.

Techniques of Variational Analysis

Techniques of Variational Analysis PDF Author: Jonathan Borwein
Publisher: Springer Science & Business Media
ISBN: 0387282718
Category : Mathematics
Languages : en
Pages : 368

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Book Description
Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis Provides a good introduction to the topic

Variational Methods in Nonlinear Analysis

Variational Methods in Nonlinear Analysis PDF Author: Dimitrios C. Kravvaritis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110647451
Category : Mathematics
Languages : en
Pages : 584

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Book Description
This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.

Variational Methods in Economics

Variational Methods in Economics PDF Author: George Hadley
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages :

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Book Description


Network Economics

Network Economics PDF Author: Anna Nagurney
Publisher: Springer Science & Business Media
ISBN: 1475730055
Category : Business & Economics
Languages : en
Pages : 423

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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.

Variational and Quasi-Variational Inequalities in Mechanics

Variational and Quasi-Variational Inequalities in Mechanics PDF Author: Alexander S. Kravchuk
Publisher: Springer Science & Business Media
ISBN: 1402063776
Category : Technology & Engineering
Languages : en
Pages : 337

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Book Description
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.

Variational Methods in Partially Ordered Spaces

Variational Methods in Partially Ordered Spaces PDF Author: Alfred Göpfert
Publisher: Springer Science & Business Media
ISBN: 0387217436
Category : Business & Economics
Languages : en
Pages : 359

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Book Description
This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.

Variational Principles in Mathematical Physics, Geometry, and Economics

Variational Principles in Mathematical Physics, Geometry, and Economics PDF Author: Alexandru Kristály
Publisher: Cambridge University Press
ISBN: 0521117828
Category : Mathematics
Languages : en
Pages : 385

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Book Description
A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.

Variational Methods in Economics

Variational Methods in Economics PDF Author: G. Hadley
Publisher:
ISBN:
Category :
Languages : en
Pages : 378

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Book Description


Combined Relaxation Methods for Variational Inequalities

Combined Relaxation Methods for Variational Inequalities PDF Author: Igor Konnov
Publisher: Springer Science & Business Media
ISBN: 3642568866
Category : Business & Economics
Languages : en
Pages : 190

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Book Description
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.