This course is intended to give the students a background in classical optimization models with emphasis on mathematical programming and practical applications, and to introduce the students to dynamic optimization.

*Prerequisites*: ESI 4567

Two two-hour lectures meet on Tuesday and Thursday. Grades in the course will be assigned based on biweekly homework, two examinations (a mid-term and a final), and a term project. I am willing to meet outside class for consultataion on the students' term projects.

*Textbooks*: There are three primary textbooks used in this course:

- Gill, Philip E. Walter Murray, and Margaret H. Wright.
*Practical Optimization*(New York: Academic Press, 1981).

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:

- Kamien, Morton I., and Nancy L. Schwartz.
*Dynamic Optimization the Calculus of Variations and Optimal Control Theory in Economics and Management*(New York: North-Holland, 1981).

This book is also considered **essential**.

- Tu, Pierre N. V.
*Dynamic Systems An Introduction with Applications in Economics and Biology*Second Edition (New York: Springer-Verlag, 1994).

A working draft of my class notes in book form is available Optimization Book.

*Computing*: GAMS is a standard program on the department network. Further, a student version of GAMS is available with the users guide at a reasonable price. Mathematica and Gauss
will be also be used extensively. Both programs are available on the DEC. Gauss is also available over the departmental network. A student version of Mathematica is available at the Technology Hub.

*Grades*: The grade for this class will be assigned based on two examinations, a term project, class participation, and homework as follows:

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.

- Static Optimization
- Overview of Optimality (
*2 Lectures*) - Review of Linear Algebra (
*2 Lectures*) - Optimality Conditions (
*4 Lectures*) - Algorithms (
*4 Lectures*) - Optimization on a Computer (
*2 Lectures*) - Mathematical Definition of the Dual

- Overview of Optimality (
- Dynamic Optimization
- A Review of Dynamic Mathematics (
*4 Lectures*) - Calculus of Variations (
*4 Lectures*) - Optimal Control (
*5 Lectures*) - Applications of Optimal Control Theory (
*2 Lectures*)

- A Review of Dynamic Mathematics (

Class notes will be offered in PDF format. To display these documents on your screen you will require Adobe . The docuements can be printed either with a Adobe PostScript card in a printer or ghostcript.

Wwwstat – AEB 6533 Stats

## Miami |