Work

Convex relaxation for the generalized maximum-entropy sampling problem

Year: 2026

Type: article

Abstract: The generalized maximum-entropy sampling problem (GMESP) is to select an order- s principal submatrix from an order- n covariance matrix, to maximize the product of its t greatest eigenvalues, $$0 0 < t ≤ s < n . Introduced more than 25 years ago, GMESP is a natural generalization of two fundamental problems in statistical design theory: (i) maximum-entropy sampling problem (MESP); (ii) binary D-optimality (D-Opt). In the general case, it can be motivated by a selection problem in the context of principal component analysis (PCA). We introduce the first convex-optimization based relaxation for GMESP, study its behavior, compare it to an earlier spectral bound, and demonstrate its use in a branch-and-bound scheme. We find that such an approach is practical when $$s-t$$ s - t is very small.

Source: Algorithmica

DOI: 10.1007/s00453-026-01373-9

Authors: Gabriel Ponte, Marcia Fampa, Jon Lee

Institutions: University of Michigan, Universidade Federal do Rio de Janeiro

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Conselho Nacional de Desenvolvimento Científico e Tecnológico, Air Force Office of Scientific Research