Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning

This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence result...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2017-02, Vol.65 (3), p.794-816
Main Authors: Ying Sun, Babu, Prabhu, Palomar, Daniel P.
Format: Article
Language:English
Subjects:
Algorithms
Basic converters
Convergence
Convexity
Estimation
Linear programming
Machine learning
Majorization-minimization
Minimization
non-convex optimization
Optimization
Signal processing
Signal processing algorithms
surrogate function
Taylor series
Upper bounds
upperbounds
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Summary:This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and connection to other algorithmic frameworks are also covered. To bridge the gap between theory and practice, upperbounds for a large number of basic functions, derived based on the Taylor expansion, convexity, and special inequalities, are provided as ingredients for constructing surrogate functions. With the pre-requisites established, the way of applying MM to solving specific problems is elaborated by a wide range of applications in signal processing, communications, and machine learning.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2016.2601299