#### Date of Award

1994

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics

#### First Advisor

Guillermo Ferreyra

#### Abstract

The purpose of this dissertation is to study two different generalizations of the optimal control problem based on the Vidale-Wolfe Advertising Model. The first problem is an infinite horizon free endpoint one-dimensional version of the Vidale-Wolfe optimal control problem of advertising in time varying markets. A solution is obtained for this problem. Then a thorough proof using the method of dynamic programming is presented to verify that this solution is optimal under reasonable market conditions. The second problem is a finite time fixed endpoint two-dimensional version of the Vidale-Wolfe optimal control problem. Normal optimal trajectories are obtained for this problem. A thorough proof using the Pontryagin Maximum Principle is then presented under reasonable market conditions.

#### Recommended Citation

Edie, Richard Dale, "Generalizations of the Optimal Control Problem for the Vidale-Wolfe Advertising Model." (1994). *LSU Historical Dissertations and Theses*. 5792.

http://digitalcommons.lsu.edu/gradschool_disstheses/5792

#### Pages

101