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 function 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.
Citation
Research Report RC22892, IBM T.J. Watson Research Center, Yorktown Heights NY, September 2003. To appear in "MODA 7 - Advances in Model-Oriented Design and Analysis", Contributions to Statistics, Springer, Berlin, 2004.