A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems
This paper extends a result of isolated calmness for nuclear norm regularized convex optimization problems to Ky Fan $ k $-norm regularized convex optimization problems. We find that there exists a certain equivalence relationship among the critical cones of the Ky Fan $ k $-norm function and its co...
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| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025227 |
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| author | Ziran Yin Chongyang Liu Xiaoyu Chen Jihong Zhang Jinlong Yuan |
| author_facet | Ziran Yin Chongyang Liu Xiaoyu Chen Jihong Zhang Jinlong Yuan |
| author_sort | Ziran Yin |
| collection | DOAJ |
| description | This paper extends a result of isolated calmness for nuclear norm regularized convex optimization problems to Ky Fan $ k $-norm regularized convex optimization problems. We find that there exists a certain equivalence relationship among the critical cones of the Ky Fan $ k $-norm function and its conjugate as well as the 'sigma term', namely, the conjugate function of the parabolic second-order directional derivative of the Ky Fan $ k $-norm. By establishing the equivalence between the primal (dual) strict Robinson constraint qualification (SRCQ) and the dual (primal) second-order sufficient condition (SOSC), we derive a series of complete characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for Ky Fan $ k $-norm regularized convex matrix optimization problems. The obtained results enrich the stability theory of the Ky Fan $ k $-norm regularized convex optimization problems and further enhance the usability of the related algorithms. |
| format | Article |
| id | doaj-art-5e29c672cbe7418684bc50f820ae6c2f |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-5e29c672cbe7418684bc50f820ae6c2f2025-08-20T03:16:57ZengAIMS PressAIMS Mathematics2473-69882025-03-011034955496910.3934/math.2025227A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problemsZiran Yin0Chongyang Liu1Xiaoyu Chen2Jihong Zhang3Jinlong Yuan4School of Science, Dalian Maritime University, Dalian, Liaoning, 116026, ChinaSchool of Mathematics and Information Science, Shandong Technology and Business University, Yantai, Shandong, 264005, ChinaSchool of Science, Dalian Maritime University, Dalian, Liaoning, 116026, ChinaSchool of Science, Shenyang Ligong University, Shenyang, Liaoning, 110159, ChinaSchool of Science, Dalian Maritime University, Dalian, Liaoning, 116026, ChinaThis paper extends a result of isolated calmness for nuclear norm regularized convex optimization problems to Ky Fan $ k $-norm regularized convex optimization problems. We find that there exists a certain equivalence relationship among the critical cones of the Ky Fan $ k $-norm function and its conjugate as well as the 'sigma term', namely, the conjugate function of the parabolic second-order directional derivative of the Ky Fan $ k $-norm. By establishing the equivalence between the primal (dual) strict Robinson constraint qualification (SRCQ) and the dual (primal) second-order sufficient condition (SOSC), we derive a series of complete characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for Ky Fan $ k $-norm regularized convex matrix optimization problems. The obtained results enrich the stability theory of the Ky Fan $ k $-norm regularized convex optimization problems and further enhance the usability of the related algorithms.https://www.aimspress.com/article/doi/10.3934/math.2025227isolated calmnessky fan $ k $-normcritical conesecond-order sufficient conditionstrict robinson constraint qualification |
| spellingShingle | Ziran Yin Chongyang Liu Xiaoyu Chen Jihong Zhang Jinlong Yuan A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems AIMS Mathematics isolated calmness ky fan $ k $-norm critical cone second-order sufficient condition strict robinson constraint qualification |
| title | A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems |
| title_full | A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems |
| title_fullStr | A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems |
| title_full_unstemmed | A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems |
| title_short | A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems |
| title_sort | comprehensive characterization of the robust isolated calmness of ky fan k norm regularized convex matrix optimization problems |
| topic | isolated calmness ky fan $ k $-norm critical cone second-order sufficient condition strict robinson constraint qualification |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025227 |
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