Constrained EM algorithm with projection method

Abstract

This paper proposes a new step called the P-step to handle the linear or nonlinear equality constraint in addition to the conventional EM algorithm. This new step is easy to implement, first because only the first derivatives of the object function and the constraint function are necessary, and secondly, because the P-step is carried out after the conventional EM algorithm. The estimate sequence produced by our method enjoys a monotonic increase in the observed likelihood function. We apply the P-step in addition to the conventional EM algorithm to the two illustrative examples. The first example has a linear constraint function. The second has a nonlinear constraint function. We show finally that there exists a Kuhn–Tucker vector at the limit point produced by our method.