The robust isolated calmness of spectral norm regularized convex matrix optimization problems
This article aims to provide a series of characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for spectral norm regularized convex optimization problems. By establishing the variational properties of the spectral norm function, we directly prove that the KKT mapp...
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De Gruyter
2025-08-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0189 |
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| author | Yin Ziran Chen Xiaoyu Zhang Jihong |
| author_facet | Yin Ziran Chen Xiaoyu Zhang Jihong |
| author_sort | Yin Ziran |
| collection | DOAJ |
| description | This article aims to provide a series of characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for spectral norm regularized convex optimization problems. By establishing the variational properties of the spectral norm function, we directly prove that the KKT mapping is isolated calm if and only if the strict Robinson constraint qualification (SRCQ) and the second-order sufficient condition (SOSC) hold. Furthermore, we obtain the crucial result that the SRCQ for the primal/dual problem and the SOSC for the dual/primal problem are equivalent. The obtained results can derive more equivalent conditions of the robust isolated calmness of the KKT mapping, thereby enriching the stability theory of spectral norm regularized optimization problems and enhancing the usability of isolated calmness in algorithm applications. |
| format | Article |
| id | doaj-art-2bd72bae83e8430d84b6e7cc21d2fdd8 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-2bd72bae83e8430d84b6e7cc21d2fdd82025-08-20T04:03:17ZengDe GruyterOpen Mathematics2391-54552025-08-0123126327210.1515/math-2025-0189The robust isolated calmness of spectral norm regularized convex matrix optimization problemsYin Ziran0Chen Xiaoyu1Zhang Jihong2School of Science, Dalian Maritime University, Dalian, Liaoning, 116026, P. R. ChinaSchool of Science, Dalian Maritime University, Dalian, Liaoning, 116026, P. R. ChinaSchool of Science, Shenyang Ligong University, Shenyang, Liaoning, 110159, P. R. ChinaThis article aims to provide a series of characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for spectral norm regularized convex optimization problems. By establishing the variational properties of the spectral norm function, we directly prove that the KKT mapping is isolated calm if and only if the strict Robinson constraint qualification (SRCQ) and the second-order sufficient condition (SOSC) hold. Furthermore, we obtain the crucial result that the SRCQ for the primal/dual problem and the SOSC for the dual/primal problem are equivalent. The obtained results can derive more equivalent conditions of the robust isolated calmness of the KKT mapping, thereby enriching the stability theory of spectral norm regularized optimization problems and enhancing the usability of isolated calmness in algorithm applications.https://doi.org/10.1515/math-2025-0189isolated calmnesssecond-order sufficient conditionspectral normstrict robinson constraint qualificationcritical cone90c2590c3165k10 |
| spellingShingle | Yin Ziran Chen Xiaoyu Zhang Jihong The robust isolated calmness of spectral norm regularized convex matrix optimization problems Open Mathematics isolated calmness second-order sufficient condition spectral norm strict robinson constraint qualification critical cone 90c25 90c31 65k10 |
| title | The robust isolated calmness of spectral norm regularized convex matrix optimization problems |
| title_full | The robust isolated calmness of spectral norm regularized convex matrix optimization problems |
| title_fullStr | The robust isolated calmness of spectral norm regularized convex matrix optimization problems |
| title_full_unstemmed | The robust isolated calmness of spectral norm regularized convex matrix optimization problems |
| title_short | The robust isolated calmness of spectral norm regularized convex matrix optimization problems |
| title_sort | robust isolated calmness of spectral norm regularized convex matrix optimization problems |
| topic | isolated calmness second-order sufficient condition spectral norm strict robinson constraint qualification critical cone 90c25 90c31 65k10 |
| url | https://doi.org/10.1515/math-2025-0189 |
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