Term of Award
Spring 2009
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
Goran Lesaja
Committee Member 1
Billur Kaymalcalan
Committee Member 2
Scott Kersey
Committee Member 3
Yan Wu
Abstract
In this thesis the Interior -- Point Method (IPM) for Linear Programming problem (LP) that is based on the generic kernel function is considered. The complexity (in terms of iteration bounds) of the algorithm is first analyzed for a class of kernel functions defined by (3-1). This class is fairly general; it includes classical logarithmic kernel function, prototype self-regular kernel function as well as non-self-regular functions, thus it serves as a unifying frame for the analysis of IPM. Historically, most results in the theory of IPM are based on logarithmic kernel functions while other two classes are more recent. They were considered with the intention to improve theoretical and practical performance of IPMs. The complexity results that are obtained match the best known complexity results for these methods. Next, the analysis of the IPM was summarized and performed for three more kernel functions. For two of them we again matched the best known complexity results. The theoretical concepts of IPM were illustrated by basic implementation for the classical logarithmic kernel function and for the parametric kernel function both described in (3-1). Even this basic implementation shows potential for a good performance. Better implementation and more numerical testing would be necessary to draw more definite conclusions. However, that was not the goal of the thesis, the goal was to show that IPM with kernel functions different than classical logarithmic kernel function can have best known theoretical complexity.
Recommended Citation
Tanksley, Latriece Y., "Interior Point Methods and Kernel Functions of a Linear Programming Problem" (2009). Electronic Theses and Dissertations. 650.
https://digitalcommons.georgiasouthern.edu/etd/650
Research Data and Supplementary Material
No
