Cardinality-constrained structured data-fitting problems
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 algori...
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| Format: | Article |
| Language: | English |
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Université de Montpellier
2024-05-01
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| Series: | Open Journal of Mathematical Optimization |
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| Online Access: | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.27/ |
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| _version_ | 1825205136799039488 |
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| author | Fan, Zhenan Fang, Huang Friedlander, Michael P. |
| author_facet | Fan, Zhenan Fang, Huang Friedlander, Michael P. |
| author_sort | Fan, Zhenan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0590b0b505494fdcbafefd4aa45bf074 |
| institution | Kabale University |
| issn | 2777-5860 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Université de Montpellier |
| record_format | Article |
| series | Open Journal of Mathematical Optimization |
| spelling | doaj-art-0590b0b505494fdcbafefd4aa45bf0742025-02-07T14:01:17ZengUniversité de MontpellierOpen Journal of Mathematical Optimization2777-58602024-05-01512110.5802/ojmo.2710.5802/ojmo.27Cardinality-constrained structured data-fitting problemsFan, Zhenan0Fang, Huang1Friedlander, Michael P.2The University of British Columbia, CanadaThe University of British Columbia, CanadaThe University of British Columbia, CanadaA 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.https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.27/convex analysissparse optimizationlow-rank optimizationprimal-retrieval |
| spellingShingle | Fan, Zhenan Fang, Huang Friedlander, Michael P. Cardinality-constrained structured data-fitting problems Open Journal of Mathematical Optimization convex analysis sparse optimization low-rank optimization primal-retrieval |
| title | Cardinality-constrained structured data-fitting problems |
| title_full | Cardinality-constrained structured data-fitting problems |
| title_fullStr | Cardinality-constrained structured data-fitting problems |
| title_full_unstemmed | Cardinality-constrained structured data-fitting problems |
| title_short | Cardinality-constrained structured data-fitting problems |
| title_sort | cardinality constrained structured data fitting problems |
| topic | convex analysis sparse optimization low-rank optimization primal-retrieval |
| url | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.27/ |
| work_keys_str_mv | AT fanzhenan cardinalityconstrainedstructureddatafittingproblems AT fanghuang cardinalityconstrainedstructureddatafittingproblems AT friedlandermichaelp cardinalityconstrainedstructureddatafittingproblems |