An assembly and decomposition approach for constructing separable minorizing functions in a class of MM algorithms

Abstract

The minorization–maximization (MM) principle provides a powerful tool for optimization in statistical applications. A challenging and subjective issue in developing an MM algorithm is to construct an appropriate minorizing function. For numerical convenience, our (AD) approach to constructing the minorizing function as the sum of separable univariate functions yields general class of MM algorithms. We employ the assembly technique (A-technique) and the decomposition technique (D-technique). The A-technique introduces a bank of complemental assembly functions which are often the building blocks of various MM algorithms. The D-technique decomposes the objective function into three parts and separately minorizes them. We illustrate the utility of the proposed approach in multiple applications. Numerical experiments demonstrate its advantages.