Prerequisites: ESI 4567
Instructor: Charles B. Moss
1130B McCarty Hall
Phone: 392-1845 Ext 404
Email: cbmoss@ifas.ufl.edu
This book will be used extensively in the first half of the course
and will be considered essential. The theoretical development
of the calculus of variations and optimal control follows with
most of this material as presented in:
This book is also considered essential.
Will be used to review the mathematics of dynamic systems. Other
materials such as lecture notes will be made available on the
internet at http://kierkegaard.ifas.ufl.edu/chuck/aeb6533.mathprogramming/syllbus.html.
| Mid - Term Examination | |
| Final Examination | |
| Term Project | |
| Homework | |
| Class Participation |
Homework will be due in two week increments. Each assignment will be handed
out at the beginning of each increment and will involve topics
covered over that time span. For example, the first assignment
will involve the derivation of the first and second order necessary
conditions for an unconstrained mathematical formulation. The
term project consists of two components (1) a written paper of
a relevant application of static or dynamic optimization and (2)
an oral presentation of the results in class. The intent of this
project is to prepare the student for the contributed paper process
followed by most academic societies. The 5% assigned to class
participation is intended to guarantee that the students are attending
classes and keeping up with the readings.
Readings: Gill, Murray and Wright section 2.3 pp. 45-58.
Food and Diet, Farm and Agribusiness Management, Farm Firm Development, and Production Response PDF, Overheads
Notes from Agricultural Risk Analysis and Decision Making AEB 6182
The Farm Portfolio Problem Part I: The Expected Value-Variance Frontier PDF, Overheads
The Farm Portfolio Problem Part II: MOTAD and Direct Utility Maximization PDF, Overheads
The Farm Portfolio Problem Part III: Target MOTAD and Discrete Sequential Stochastic Programming PDF, Overheads
Interregtional and Spatial Economics, Econometrics and Statistical Applications, Policy Analysis, and Nonparametric Efficiency Analysis PDF, Overheads
Applied General Equilibrium Notes
A Mathematica notebook demonstrating the error of a second order Taylor series expansion for a cubic polynomical. Notebook, PDF
See also lecture notes from AEB 6592
A MatLab program demonstrating row reduction and the use of elementry matrices. MatLab Program
A Mathematica notebook demonstrating the concept of spanning and alternative basis for the same spanned space (also demonstrates the used of substitution rules in Mathematica) Notebook,PostScript,PDF
Notes on matrix factorizations PostScript, PDF
A Matlab program demonstrating LU factorizations and solving of system equations MatLab Program
Review of Matrix Algebra and Vector Spaces: Lecture XXIV from Mathematical Statistics AEB 6933
Exercise 1 - Taylor Series Expansion
Assignment PDF
Solution Notebook,PostScript
SPECS file for Minos solution of simple farm planning model SPECS File
Fortran program to call Minos Fortran Program
A Mathematica notebook for deriving the characteristic equation and eigenvalues of a matrix Mathematica Notebook
Practice Problems PDF
Solutions Notebook,PostScript
Also See Simon, C.P. and L. Blume Mathematics for Economists New York: W.W. Norton & Company, 1994.
A Mathematica notebook depicting the application of unconstrained and linearly constrained multivariate optimization conditions Notebook
Some examples of nullspaces
A Gauss program to demonstrate nullspaces
Excel Spreadsheet depicting how the economic surplus model is derived Excel File
Gauss file demonstrating the optimality conditions on a single market Gauss File
GAMS file solving for the optimal combination of production and consumption GAMS File
GAMS output file solvingin for the optimal combination of production and consumption GAMS Output
A Mathematica notebook depicting the application of linear inequality constrained necessary conditions Notebook
Mathematica notebook to develop the concept of a linear approximation to the nonlinear constraint Notebook
Mathematica notebook demonstrating the first and second order necessary conditions for nonlinear equality constraints Notebook
Excel spreadsheet solving the farm portfolio problem Excel File
GAMS solution of the Household Production Model GAMS File , Solution File
Gauss code for First and Second Order Necessary Conditions for the Freund formulation Gauss File
Minos 5.5 code for Freund formulation Fortran Program, Specs File, Output File
A mathematica notebook on univariate optimization Notebook
A mathematica notebook on multivariate algorithms including Newton-Raphson and Steepest Descent Notebook
Explanation of the conjugate gradient technique PostScript,PDF
A Comparison of various conjugate gradient convergence performance Notebook
Maximizing utility subject to a linear inequality constraint in Gauss Gauss File
A sample of GAMS is available online.
Examples of nonlinear objective functions with linear equality and inequality constraints
Minimize the variance for a given level of income and land empir1.gms
Freund's formulation of the certainty equivalence of a farm plan empir2.gms
Direct utility maximization empir3.gms
Minimize the variance on a stock portfolio Fortran Program,SPECS File
Maximize utility subject to a nonlinear budget constraint Fortran Program,SPECS
Maximize expected utility Fortran File,SPECS
Readings Tu Chapters 2 and 3, and 5 and 6 pp. 5-57 and 83-161.

