Lange K. MM Optimization Algorithms 2016

Textbook in PDF format

MM Optimization Algorithms offers an overview of the MM principle, a device for deriving optimization algorithms satisfying the ascent or descent property. These algorithms can separate the variables of a problem, avoid large matrix inversions, linearize a problem, restore symmetry, deal with equality and inequality constraints gracefully, and turn a nondifferentiable problem into a smooth problem.
The author presents the first extended treatment of MM algorithms, which are ideal for high-dimensional optimization problems in data mining, imaging, and genomics; derives numerous algorithms from a broad diversity of application areas, with a particular emphasis on statistics, biology, and data mining; and summarizes a large amount of literature that has not reached book form before.
Audience: This book is intended for those interested in high-dimensional optimization. Background material on convexity and semidifferentiable functions is derived in a setting congenial to graduate students.
Beginning Examples;
Convexity and Inequalities;
Nonsmooth Analysis;
Majorization and Minorization;
Proximal Algorithms;
Regression and Multivariate Analysis;
Convergence and Acceleration;
Mathematical Background