Cardinality-constrained structured data-fitting problems

TL;DR

This paper introduces a memory-efficient framework for solving cardinality-constrained structured data-fitting problems, using dual-based rules to efficiently derive near-optimal primal solutions from dual solutions, supported by theoretical guarantees and real-world experiments.

Contribution

It presents a novel dual-based approach with atom-identification rules that efficiently produce feasible primal solutions under cardinality constraints, with proven guarantees.

Findings

The proposed method is computationally cheap and scalable.

Numerical experiments confirm the approach's efficiency and accuracy.

The framework provides rigorous guarantees for near-optimal solutions.

Abstract

A memory-efficient framework is described for the cardinality-constrained structured data-fitting problem. Dual-based atom-identification rules are proposed that reveal the structure of the optimal primal solution from near-optimal dual solutions. These rules allow for a simple and computationally cheap algorithm for translating any feasible dual solution to a primal solution that satisfies the cardinality constraint. Rigorous guarantees are provided for obtaining a near-optimal primal solution given any dual-based method that generates dual iterates converging to an optimal dual solution. Numerical experiments on real-world datasets support confirm the analysis and demonstrate the efficiency of the proposed approach.