Date of Award
Summer 2007
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics & 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.
Rights
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DOI
10.25777/m5m4-vz09
ISBN
9780549218265
Recommended Citation
Thomas, William H..
"On the Use of Quasi-Newton Methods for the Minimization of Convex Quadratic Splines"
(2007). Doctor of Philosophy (PhD), Dissertation, Mathematics & Statistics, Old Dominion University, DOI: 10.25777/m5m4-vz09
https://digitalcommons.odu.edu/mathstat_etds/64