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.
https://repository.lsu.edu/gradschool_disstheses/5792
Pages
101
DOI
10.31390/gradschool_disstheses.5792