New bounds for subset selection from conic relaxations

New bounds are proposed for the subset selection problem which consists in minimizing the residual sum of squares subject to a cardinality constraint on the maximum number of non-zero variables. They rely on new convex relaxations providing both upper and lower bounds that are compared with others present in the literature. The performance of these methods is illustrated through computational experiments. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This article proposes new bounds for the subset selection problem, which aims to minimize the residual sum of squares while considering the constraint on the maximum number of non-zero variables. The study introduces new convex relaxations that provide both upper and lower bounds and compares them with existing methods in the literature. The performance of these methods is demonstrated through computational experiments.