Two classes of multiplicative algorithms for constructing optimizing distributions

We construct approximate optimizing distributions (pj)pj by maximizing a criterion function subject to the basic constraints on pjpj of nonnegativity and summation to unity. We use a class of multiplicative algorithms, indexed by a function f(.)f(.), which depends on the derivatives of the criterion function. The function may depend on one or more free parameters. To improve the convergence, we consider two approaches—Approach I and Approach II. Approach II is reported in Torsney and Mandal [2004. Multiplicative algorithms for constructing optimizing distributions: further developments. In: Bucchianico, A.D., Läuter, H., Wynn, H.P. (Ed.), MODA 7—Advances in Model-Oriented Design and Analysis. Physica, Heidelberg, pp. 163–171]. In Approach I, the criterion function can have only positive partial derivatives, whereas in Approach II the criterion can have both positive and negative derivatives. We consider objective choices of the class of functions f(.)f(.) for the two approaches. Considerable improvements in convergence are seen for each of the approaches.