  We show that proximal minimization algorithms (PMA), majorization
minimization (MM), and alternating minimization (AM) are equivalent. Each type
of algorithm leads to a decreasing sequence of objective function. New
conditions on PMA are given (the limit of the decreasing sequence of objective
function is indeed the infimum of the objective function), which lead to new
conditions on AM for the sequence Phi to converge to its infimum. These
conditions can then be translated into the language of MM. Examples are given
of each type of algorithm and some open questions are posed.
