Mixing convex-optimization bounds for maximum-entropy sampling

• Published in: Mathematical programming Vol. 188; no. 2; pp. 539 - 568
• Main Authors: Chen, Zhongzhu, Fampa, Marcia, Lambert, Amélie, Lee, Jon
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021; Springer Nature B.V; Springer Verlag
• Subjects: Calculus of Variations and Optimal Control; Optimization; Combinatorial analysis; Combinatorics; Convexity; Covariance matrix; Entropy; Exact solutions; Full Length Paper; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Optimization; Optimization and Control; Sampling; Theoretical; Upper bounds; Mixing; 90C51; Convex optimization; 90C25; Maximum-entropy sampling; 90C27; 62H11; 62K99; maximum-entropy sampling; convex optimization Mathematics Subject Classification 90C25
• ISSN: 0025-5610; 1436-4646; 1436-4646
• DOI: 10.1007/s10107-020-01588-w

The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order- s principal submatrix of an order- n covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on convex optimization. We present a methodology for “mixing” these bounds to achieve better bounds.