Term of Award
Spring 2021
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (restricted to Georgia Southern)
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
Emil Iacob
Committee Member 2
Goran Lesaja
Abstract
This thesis investigates a new approach to the optimization of functions using only data defined on sparse grids. The sparse grids provide a dramatic reduction in data compared to full grids, and spline interpolants are constructed to serve as accurate and smooth surrogates to the underlying functions being optimized. Using this approach, the number of grid points needed for approximation and optimization is significantly reduced without greatly compromising accuracy. In this thesis, we provide an overview of sparse grids, spline interpolation and optimization methods that are pertinent to our algorithm's development. We test several built-in optimizers in MATLAB, and implement our own conjugate gradient method using different choices for descent directions with an inexact line search based on the Armijo step length. We provide theoretical and numerical results using data from several test functions to demonstrate algorithm performance.
Recommended Citation
Ehirim, Chukwugozirim, "Spline Interpolation and Optimization on Sparse Grids" (2021). Electronic Theses and Dissertations. 2253.
https://digitalcommons.georgiasouthern.edu/etd/2253
Research Data and Supplementary Material
No
