Constructing optimal designs with constraints

We construct constrained approximate optimal designs by maximizing a criterion subject to constraints. We approach this problem by transforming the constrained optimization problem to one of maximizing three functions of the design weights simultaneously. We used a class of multiplicative algorithms, indexed by a function f(·). These algorithms are shown to satisfy the basic constraints on the design weights of nonnegativity and summation to unity. We also investigate techniques for improving convergence rates by means of some suitable choices of the function f(·).