  We consider a class of convex optimization problems over the simplex of
probability measures. Our framework comprises optimal experimental design (OED)
problems, in which the measure over the design space indicates which
experiments are being selected. Due to the presence of additional bound
constraints, the measure possesses a Lebesgue density and the problem can be
cast as an optimization problem over the space of essentially bounded
functions. For this class of problems, we consider two first-order methods
including FISTA and a proximal extrapolated gradient method, along with
suitable stopping criteria. Finally, acceleration strategies targeting the
dimension of the subproblems in each iteration are discussed. Numerical
experiments accompany the analysis throughout the paper.
