Date of Award
Mathematics and Statistics
Mau Nam Nguyen
Mathematical optimization, Convex functions
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.
Giles, Daniel, "The Majorization Minimization Principle and Some Applications in Convex Optimization" (2015). University Honors Theses. Paper 152.