2010 | OriginalPaper | Buchkapitel
The MM Algorithm
verfasst von : Kenneth Lange
Erschienen in: Numerical Analysis for Statisticians
Verlag: Springer New York
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Most practical optimization problems defy exact solution. In the current chapter we discuss an optimization method that relies heavily on convexity arguments and is particularly useful in high-dimensional problems such as image reconstruction [27]. This iterative method is called the MM algorithm. One of the virtues of the MM acronym is that it does double duty. In minimization problems, the first M stands for majorize and the second M for minimize. In maximization problems, the first M stands for minorize and the second M for maximize. When it is successful, the MM algorithm substitutes a simple optimization problem for a difficult optimization problem. Simplicity can be attained by (a) avoiding large matrix inversions, (b) linearizing an optimization problem, (c) separating the variables of an optimization problem, (d) dealing with equality and inequality constraints gracefully, and (e) turning a nondifferentiable problem into a smooth problem. In simplifying the original problem, we pay the price of iteration or iteration with a slower rate of convergence.