First-Order Methods for Optimal Experimental Design Problems with Bound Constraints

Abstract: 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.