ABSTRACT
The objective function in the maximum likelihood estimator (MLE) problem is the likelihood or the log-likelihood function. Some optimization problems can be solved analytically. There are several approaches to one-dimensional optimization implemented in R. Many types of problems can be restated so that the root-finding function uniroot can be applied. The Expectation–Maximization (EM) algorithm is a general optimization method that is often applied to find maximum likelihood estimates when data are incomplete. The main idea of the EM algorithm is simple, and although it may be slow to converge relative to other available methods, it is reliable at finding a global maximum. The simplex method is a widely applied optimization method for a special class of constrained optimization problems with linear objective functions and linear constraints. The constraints usually include inequalities, and therefore the region over which the objective function is to be optimized can be described by a simplex.
