The maximum feasible subset problem (maxFS) and applications

Abstract

The maximum feasible subset problem (maxFS) is this: given an infeasible set of constraints, find a largest cardinality subset that admits a feasible solution. This problem is NP-hard but has been studied extensively for the case of linear constraints, and good heuristic solution algorithms are available. There is a surprisingly large range of applications for algorithms that solve the linear maxFS problem, including analyzing infeasible linear programs, finding the data depth, placing separating hyperplanes in classification decision trees, recovering sparse data in compressed sensing, dimension reduction in nonnegative matrix factorization, etc. This paper reviews maxFS solution algorithms, and surveys the existing and new applications.