Date of Award

Summer 2007

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

John J. Swetits

Committee Member

Wu Li

Committee Member

Hideaki Kaneko

Committee Member

Przemek Bogacki

Abstract

In reformulating a strictly convex quadratic program with simple bound constraints as the unconstrained minimization of a strictly convex quadratic spline, established algorithms can be implemented with relaxed differentiability conditions. In this work, the positive definite secant update method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) is investigated as a tool to solve the unconstrained minimization problem. It is shown that there is a linear convergence rate and, for nondegenerate problems, the process terminates in a finite number of iterations. Numerical examples are provided.

DOI

10.25777/m5m4-vz09

ISBN

9780549218265

Included in

Mathematics Commons

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