Mixing convex-optimization bounds for maximum-entropy sampling

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 b...

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Bibliographic Details
Published inMathematical programming Vol. 188; no. 2; pp. 539 - 568
Main Authors Chen, Zhongzhu, Fampa, Marcia, Lambert, Amélie, Lee, Jon
Format Journal Article
LanguageEnglish
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
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-020-01588-w