Open Journal of Mathematical Optimization

Cardinality-constrained structured data-fitting problems
Zhenan Fan1; Huang Fang1; Michael P. Friedlander1
1 The University of British Columbia, Canada
Open Journal of Mathematical Optimization, Volume 5 (2024), article no. 2, 21 p.

A memory-efficient solution framework is proposed for the cardinality-constrained structured data-fitting problem. Dual-based atom-identification rules reveal the structure of the optimal primal solution from near-optimal dual solutions, which allows for a simple and computationally efficient algorithm that translates any feasible dual solution into a primal solution satisfying the cardinality constraint. Rigorous guarantees bound the quality of 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 the analysis and demonstrate the efficiency of the proposed approach.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/ojmo.27
Keywords: convex analysis, sparse optimization, low-rank optimization, primal-retrieval
Zhenan Fan 1; Huang Fang 1; Michael P. Friedlander 1

1 The University of British Columbia, Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Zhenan Fan; Huang Fang; Michael P. Friedlander. Cardinality-constrained structured data-fitting problems. Open Journal of Mathematical Optimization, Volume 5 (2024), article  no. 2, 21 p. doi : 10.5802/ojmo.27. https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.27/

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