Date of Award

2015

Document Type

Thesis

Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors

Department

Mathematics

First Advisor

Mau Nam Nguyen

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.

Persistent Identifier

http://archives.pdx.edu/ds/psu/15436

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