Date of Award
Doctor of Philosophy (PhD)
Mathematics and Statistics
Computational and Applied Mathematics
John J. Swetits
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.
Thomas, William H..
"On the Use of Quasi-Newton Methods for the Minimization of Convex Quadratic Splines"
(2007). Doctor of Philosophy (PhD), Dissertation, Mathematics and Statistics, Old Dominion University, DOI: 10.25777/m5m4-vz09