The Majorization Minimization Principle and Some Applications in Convex Optimization

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.

A New Compressive Sensing Method for Speckle Reducing in Complex-valued SAR Data

“…The log term is concave and can be approximated by its first Taylor expansion using the Majorization Minimization (MM) approach [21]. For that, an iteratively re-weighted formulation of the optimization problem is given by…”