Using continuous nonlinear relaxations to solve. constrained maximum-entropy sampling problems

We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Prob- lem - the problem of choosing the s x s principal submatrix with maximal determinant from a given n x n positive definite matrix, subject to linear constraints. We implement a branch-and- bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation. A parallel implementation of the algorithm exhibits approximately linear speed-up for up to 8 processors, and has successfully solved problem instances which were heretofore intractable.

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