A masked spectral bound for maximum-entropy sampling

We introduce a new "masked spectral bound" for the maximum entropy sampling problem. This bound is a continuous generalization of the very effective "spectral partition bound". Optimization of the masked spectral bound requires the minimization of a nonconvex, nondifferentiable objective over a semidefiniteness constraint. We describe a nonlinear affine scaling algorithm to approximately minimize the bound. Implementation of the procedure obtains excellent bounds at modest computational expense.