Variational Methods In Economics
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Variational Methods In Economics
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Author : G. Hadley
language : en
Publisher: Elsevier
Release Date : 2014-07-22
Variational Methods In Economics written by G. Hadley and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Business & Economics categories.
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
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Author : George Hadley
language : en
Publisher:
Release Date : 1971
Variational Methods In Economics written by George Hadley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Calculus of variations categories.
Variational Methods In Economics
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Author : G. Hadley
language : en
Publisher:
Release Date : 1971
Variational Methods In Economics written by G. Hadley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Variational Methods In Mathematical Physics
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Author : Philippe Blanchard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational Methods In Mathematical Physics written by Philippe Blanchard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).
Variational Methods In Statistics
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Author : Rustagi
language : en
Publisher: Academic Press
Release Date : 1976-03-15
Variational Methods In Statistics written by Rustagi and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-03-15 with Computers categories.
Variational Methods in Statistics
Numerical Methods In Economics
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Author : Kenneth L. Judd
language : en
Publisher: MIT Press
Release Date : 1998-09-28
Numerical Methods In Economics written by Kenneth L. Judd and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-28 with Business & Economics categories.
To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.
Numerical Optimization
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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Numerical Optimization written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Numerical Optimization: Theories and Applications" is a comprehensive guide that delves into the fundamental principles, advanced techniques, and practical applications of numerical optimization. We provide a systematic introduction to optimization theory, algorithmic methods, and real-world applications, making it an essential resource for students, researchers, and practitioners in optimization and related disciplines. We begin with an in-depth exploration of foundational concepts in optimization, covering topics such as convex and non-convex optimization, gradient-based methods, and optimization algorithms. Building upon these basics, we delve into advanced optimization techniques, including metaheuristic algorithms, evolutionary strategies, and stochastic optimization methods, providing readers with a comprehensive understanding of state-of-the-art optimization methods. Practical applications of optimization are highlighted throughout the book, with case studies and examples drawn from various domains such as machine learning, engineering design, financial portfolio optimization, and more. These applications demonstrate how optimization techniques can effectively solve complex real-world problems. Recognizing the importance of ethical considerations, we address issues such as fairness, transparency, privacy, and societal impact, guiding readers on responsibly navigating these considerations in their optimization projects. We discuss computational challenges in optimization, such as high dimensionality, non-convexity, and scalability issues, and provide strategies for overcoming these challenges through algorithmic innovations, parallel computing, and optimization software. Additionally, we provide a comprehensive overview of optimization software and libraries, including MATLAB Optimization Toolbox, Python libraries like SciPy and CVXPY, and emerging optimization frameworks, equipping readers with the tools and resources needed to implement optimization algorithms in practice. Lastly, we explore emerging trends, future directions, and challenges in optimization, offering insights into the evolving landscape of optimization research and opportunities for future exploration.
Optimization And Stability Theory For Economic Analysis
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Author : Brian Beavis
language : en
Publisher: Cambridge University Press
Release Date : 1990
Optimization And Stability Theory For Economic Analysis written by Brian Beavis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Economics, Mathematical categories.
This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics central to economic analysis since the latter is so much concerned with the optimizing behaviour of economic agents and the stability of the interaction processes to which this gives rise. The topics covered include convexity, mathematical programming, fixed point theorems, comparative static analysis and duality, the stability of dynamic systems, the calculus of variations and optimal control theory. The authors present a more detailed and wide-ranging discussion of these topics than is to be found in the few books which attempt a similar coverage. Although the text deals with fairly advanced material, the mathematical prerequisites are minimised by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra. A novel feature of the book is that it provides the reader with an understanding and feel for the kinds of mathematical techniques most useful for dealing with particular economic problems. This is achieved through an extensive use of a broad range of economic examples (rather than the numerical/algebraic examples so often found). This is suitable for use in advanced undergraduate and postgraduate courses in economic analysis and should in addition prove a useful reference work for practising economists.
Foundations Of Dynamic Economic Analysis
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Author : Michael R. Caputo
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-10
Foundations Of Dynamic Economic Analysis written by Michael R. Caputo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-10 with Business & Economics categories.
Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.
Optimal Control Theory And Static Optimization In Economics
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Author : Daniel Léonard
language : en
Publisher: Cambridge University Press
Release Date : 1992-01-31
Optimal Control Theory And Static Optimization In Economics written by Daniel Léonard and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-31 with Business & Economics categories.
Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purpose of the book is to draw the parallel between optimal control theory and static optimization. Chapter 1 provides an extensive treatment of constrained and unconstrained maximization, with emphasis on economic insight and applications. Starting from basic concepts, it derives and explains important results, including the envelope theorem and the method of comparative statics. This chapter may be used for a course in static optimization. The book is largely self-contained. No previous knowledge of differential equations is required.