## Dynamic Economics: Optimization by the Lagrange Method

*Gregory C. Chow*

- Published in print:
- 1997
- Published Online:
- October 2011
- ISBN:
- 9780195101928
- eISBN:
- 9780199855032
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195101928.001.0001
- Subject:
- Economics and Finance, Financial Economics

This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The ... More

## Optimal Resource Allocations

*Lars Peter Hansen and Thomas J. Sargent*

### in Recursive Models of Dynamic Linear Economies

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691042770
- eISBN:
- 9781400848188
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691042770.003.0005
- Subject:
- Economics and Finance, History of Economic Thought

This chapter describes a planning problem that generates competitive equilibrium allocations and compares two methods for solving it. The first method uses state- and date-contingent Lagrange ... More

## Optimal Programming

*S. N. Afriat*

### in Logic of Choice and Economic Theory

- Published in print:
- 1987
- Published Online:
- November 2003
- ISBN:
- 9780198284611
- eISBN:
- 9780191595844
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198284616.003.0024
- Subject:
- Economics and Finance, Microeconomics

This is the first of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It introduces the general ideas of optimal programming ... More

## Dynamic Optimization in Discrete Time

*GREGORY C. CHOW*

### in Dynamic Economics: Optimization by the Lagrange Method

- Published in print:
- 1997
- Published Online:
- October 2011
- ISBN:
- 9780195101928
- eISBN:
- 9780199855032
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195101928.003.0002
- Subject:
- Economics and Finance, Financial Economics

In dynamic economics, a set of equations are used to describe how state variables undergo dynamic evolution. This set of equations is used in maximizing a specific objective function that proves to ... More

## Entropy Maximization

*Amos Golan*

### in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199349524
- eISBN:
- 9780199349555
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199349524.003.0004
- Subject:
- Economics and Finance, Econometrics

In this chapter I develop the essential maximum entropy procedure, which is an inversion procedure for inferring an unknown probability distribution function from incomplete information. The ... More

## The principles of mechanics before Hertz

*JESPER LÜTZEN*

### in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0002
- Subject:
- Physics, History of Physics

The period until 1860 saw a steady flow of interesting new theoretical discoveries in mechanics, even in the area of mechanics of systems of finitely many mass points. Moreover, there was a continued ... More

## Testing and Evaluation

*David F. Hendry*

### in Dynamic Econometrics

- Published in print:
- 1995
- Published Online:
- November 2003
- ISBN:
- 9780198283164
- eISBN:
- 9780191596384
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198283164.003.0013
- Subject:
- Economics and Finance, Econometrics

The non‐central chi‐squared distribution frequently results when hypothesis testing, so the large‐sample properties of such tests are analysed for sequences of local alternatives. Test power depends ... More

## Economic Growth

*GREGORY C. CHOW*

### in Dynamic Economics: Optimization by the Lagrange Method

- Published in print:
- 1997
- Published Online:
- October 2011
- ISBN:
- 9780195101928
- eISBN:
- 9780199855032
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195101928.003.0003
- Subject:
- Economics and Finance, Financial Economics

Through dynamic programming, the Bellman equation could be set up from a simple optimal growth model that is subject to a constraint function which involves variables that denote consumption, capital ... More

## Models in Finance

*GREGORY C. CHOW*

### in Dynamic Economics: Optimization by the Lagrange Method

- Published in print:
- 1997
- Published Online:
- October 2011
- ISBN:
- 9780195101928
- eISBN:
- 9780199855032
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195101928.003.0007
- Subject:
- Economics and Finance, Financial Economics

Using stochastic differential equations instead of utilizing stochastic difference equations, most of the models involved in finance follow Merton’s work and are developed in continuous time. In this ... More

## A Commodity Space

*Lars Peter Hansen and Thomas J. Sargent*

### in Recursive Models of Dynamic Linear Economies

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691042770
- eISBN:
- 9781400848188
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691042770.003.0006
- Subject:
- Economics and Finance, History of Economic Thought

This chapter describes a concept of value that will be used to formulate a model in which the decisions of agents are reconciled in a competitive equilibrium. It describes a commodity space in which ... More

## Scattering by a Bounded Inhomogeneity

*Peter Monk*

### in Finite Element Methods for Maxwell's Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.003.0011
- Subject:
- Mathematics, Numerical Analysis

This chapter continues the approximation of the field scattered by a bounded object. In this case, a penetrable scatterer (i.e., not a perfect conductor) is considered and the analysis of the ... More

## A Complete Info-Metrics Framework

*Amos Golan*

### in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199349524
- eISBN:
- 9780199349555
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199349524.003.0009
- Subject:
- Economics and Finance, Econometrics

In this chapter I develop the complete info-metrics framework for inferring problems and theories under all types of uncertainty and missing information. That framework allows for uncertainty in the ... More

## Convex Programming

*S. N. Afriat*

### in Logic of Choice and Economic Theory

- Published in print:
- 1987
- Published Online:
- November 2003
- ISBN:
- 9780198284611
- eISBN:
- 9780191595844
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198284616.003.0025
- Subject:
- Economics and Finance, Microeconomics

This is the second of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It introduces convexity conditions, and shows where ... More

## 5 Testing linearity against parametric alternatives

*Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger*

### in Modelling Nonlinear Economic Time Series

- Published in print:
- 2010
- Published Online:
- May 2011
- ISBN:
- 9780199587148
- eISBN:
- 9780191595387
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199587148.003.0005
- Subject:
- Economics and Finance, Econometrics

The topic of this chapter is testing linearity of a model when the alternative is a parametric nonlinear model nesting a linear model. The case leading to standard asymptotic inference is discussed ... More

## Constrained Lagrangian Mechanics

*Peter Mann*

### in Lagrangian and Hamiltonian Dynamics

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations ... More

## Stress response in the presence of local constraints on the deformation

*David J. Steigmann*

### in Finite Elasticity Theory

- Published in print:
- 2017
- Published Online:
- December 2017
- ISBN:
- 9780198567783
- eISBN:
- 9780191746536
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198567783.003.0006
- Subject:
- Mathematics, Applied Mathematics

Chapter 6 develops the structure of the stress response in the presence of material constraints on the basis of the Lagrange-multiplier rule. Examples given include incompressibility and ... More

## Lagrangian Mechanics

*Jennifer Coopersmith*

### in The Lazy Universe: An Introduction to the Principle of Least Action

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198743040
- eISBN:
- 9780191802966
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198743040.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is ... More

## Adding a Dimension

*A. R. P. Rau*

### in The Beauty of Physics: Patterns, Principles, and Perspectives

- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709916
- eISBN:
- 9780191780189
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709916.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Dimensional considerations are a powerful, integral part of physics. Starting with the familiar linear dimension, physics expands the idea in different ways. The essence of even complicated problems ... More

## Hamiltonian Fluid Dynamics

*Rick Salmon*

### in Lectures on Geophysical Fluid Dynamics

- Published in print:
- 1998
- Published Online:
- November 2020
- ISBN:
- 9780195108088
- eISBN:
- 9780197561034
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195108088.003.0010
- Subject:
- Earth Sciences and Geography, Geophysics: Earth Sciences

In this final chapter, we return to the subject of the first: the fundamental principles of fluid mechanics. In chapter 1, we derived the equations of fluid motion from Hamilton’s principle of ... More

## Self-consistent Field Orbital Methods

*Jochen Autschbach*

### in Quantum Theory for Chemical Applications: From Basic Concepts to Advanced Topics

- Published in print:
- 2020
- Published Online:
- February 2021
- ISBN:
- 9780190920807
- eISBN:
- 9780197508350
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190920807.003.0008
- Subject:
- Chemistry, Quantum and Theoretical Chemistry

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) ... More