ADMM for 0/1 D-Opt and MESP relaxations

TL;DR

This paper introduces ADMM algorithms to efficiently solve convex relaxations of NP-hard 0/1 D-optimality and MESP problems, demonstrating their practical effectiveness through experiments.

Contribution

The paper develops ADMM-based algorithms for convex relaxations of 0/1 D-optimality and MESP problems, offering a new approach to approximate solutions.

Findings

ADMM algorithms effectively solve relaxations of complex optimization problems.

Experimental results show practical value of the proposed methods.

The approach improves upon existing convex relaxation techniques.

Abstract

The 0/1 D-optimality problem and the Maximum-Entropy Sampling problem are two well-known NP-hard discrete maximization problems in experimental design. Algorithms for exact optimization (of moderate-sized instances) are based on branch-and-bound. The best upper-bounding methods are based on convex relaxation. We present ADMM (Alternating Direction Method of Multipliers) algorithms for solving these relaxations and experimentally demonstrate their practical value.