First Advisor
Mau Nam Nguyen
Date of Award
2015
Document Type
Thesis
Degree Name
Bachelor of Science (B.S.) in Mathematics and University Honors
Department
Mathematics
Subjects
Mathematical optimization, Convex functions
DOI
10.15760/honors.175
Abstract
The majorization-minimization (MM) principle is an important tool for developing algorithms to solve optimization problems. This thesis is devoted to the study of the MM principle and applications to convex optimization. Based on some recent research articles, we present a survey on the principle that includes the geometric ideas behind the principle as well as its convergence results. Then we demonstrate some applications of the MM principle in solving the feasible point, closest point, support vector machine, and smallest intersecting ball problems, along with sample MATLAB code to implement each solution. The thesis also contains new results on effective algorithms for solving the smallest intersecting ball problem.
Rights
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Persistent Identifier
http://archives.pdx.edu/ds/psu/15436
Recommended Citation
Giles, Daniel, "The Majorization Minimization Principle and Some Applications in Convex Optimization" (2015). University Honors Theses. Paper 152.
https://doi.org/10.15760/honors.175