Solutions of Inequality Constrained Spline Optimization Problems with the Active Set Method

<p>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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2015

Author dc:creator

• Holloway, Joshua A

Contributors dc:contributor

• Xiezhang Li
• Hua Wang

• ETD
• Spline curve
• B-Spline
• Constrained optimization
• Quadratic programming
• Active set method
• Other Applied Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1308

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2373