Date of Award

8-2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Advisor

Wiecek, Margaret M

Committee Member

Calkin , Neil

Committee Member

Fadel , Georges

Committee Member

Viktorova , Irina

Committee Member

Warner , Daniel

Abstract

Applications in engineering design and the material sciences motivate the development of optimization theory in a manner that additionally draws from other branches of mathematics including the functional, complex, and numerical analyses.
The first contribution, motivated by an automotive design application, extends multiobjective optimization theory under the assumption that the problem information is not available in its entirety to a single decision maker as traditionally assumed in the multiobjective optimization literature. Rather, the problem information and the design control are distributed among different decision makers. This requirement appears in the design of an automotive system whose subsystem components themselves correspond to highly involved design subproblems each of whose performance is measured by multiple criteria. This leads to a system/subsystem interaction requiring a coordination whose algorithmic foundation is developed and rigorously examined mathematically.
The second contribution develops and analyzes a parameter estimation approach motivated from a time domain modeling problem in the material sciences. In addition to drawing from the theory of least-squares optimization and numerical analysis, the development of a mathematical foundation for comparing a baseline parameter estimation approach with an alternative parameter estimation approach relies on theory from both the functional and complex analyses.
The application of the developed theory and algorithms associated with both contributions is also discussed.

Share

COinS