Ebook: MM Optimization Algorithms

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.

Contents: Chapter 1: Beginning Examples; Chapter 2: Convexity and Inequalities; Chapter 3: Nonsmooth Analysis; Chapter 4: Majorization and Minorization; Chapter 5: Proximal Algorithms; Chapter 6: Regression and Multivariate Analysis; Chapter 7: Convergence and Acceleration; Appendix A: Mathematical Background.