This book 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. This is the first extended treatment of MM algorithms, which are ideal for high-dimensional optimization problems in data mining, imaging, and genomics. Numerous algorithms are derived from a broad set of application areas with a particular emphasis on statistics, biology, and data mining, and the author summarizes a large amount of literature which has previously been unavailable in book form. This volume is recommended for graduate students interested in high-dimensional optimization.