Efficient computational algorithms for approximate optimal designs

In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal criteria, D- and A-optimal criteria. For D-optimality, we provide an alternative proof for the monotonic convergence for D-optimal criterion and propose an efficient computational algorithm to obtain the approximate D-optimal design. We further show that the proposed algorithm converges to the D-optimal design and then proves that the approximate D-optimal design converges to the continuous D-optimal design under certain conditions. For A-optimality, we provide an efficient algorithm to obtain approximate A-optimal design and conjecture the monotonicity of the proposed algorithm. Numerical comparisons suggest that the proposed algorithms perform well and they are comparable or superior to some existing algorithms.