Generalized Scaling for the Constrained Maximum-Entropy Sampling Problem

TL;DR

This paper extends the scaling technique for the constrained maximum-entropy sampling problem, providing mathematical support and computational evidence for the effectiveness of generalized scaling in improving optimization solutions.

Contribution

It introduces generalized scaling for the problem, offers mathematical results to support algorithms, and demonstrates its practical usefulness through computational experiments.

Findings

Generalized scaling improves bounds in maximum-entropy sampling.

Mathematical results support the computation of optimal scalings.

Computational experiments show effectiveness on benchmark instances.

Abstract

The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard bound-enhancement technique in this context is scaling. We extend this technique to generalized scaling, we give mathematical results aimed at supporting algorithmic methods for computing optimal generalized scalings, and we give computational results demonstrating the usefulness of generalized scaling on benchmark problem instances.