Term of Award
Summer 2015
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Scott Kersey
Committee Member 1
Xiezhang Li
Committee Member 2
Hua Wang
Abstract
We solve the problem of finding a near-interpolant curve, subject to constraints, which minimizes the bending energy of the curve. Using B-splines as our tools, we give a brief overview of spline properties and develop several different cases of inequality constrained optimization problems of this type. In particular, we develop the active set method and use it to solve these problems, emphasizing the fact that this algorithm will converge to a solution in finite iterations. Our solution will solve an open problem regarding near-interpolant spline curves. Furthermore, we supplement this with an iterative technique for better choosing data sites so as to further minimize the bending energy of the spline curve, offering an easy solution to the problem of free data sites.
Recommended Citation
Holloway, Joshua A., "Solutions of Inequality Constrained Spline Optimization Problems with the Active Set Method" (2015). Electronic Theses and Dissertations. 1308.
https://digitalcommons.georgiasouthern.edu/etd/1308
