On the Use of Quasi-Newton Methods for the Minimization of Convex Quadratic Splines

<p>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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

2007

Author dc:creator

• Thomas, William Howard, II

Contributors dc:contributor

• John J. Swetits
• Wu Li
• Hideaki Kaneko
• Przemek Bogacki

• Convex quadratic splines
• Quasi-Newton methods
• Splines
• Mathematics

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Identifier

9780549218265

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1064