Lipschitz Modulus of Convex Functions via Function Values
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929446020186112 |
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| author | Khanh, Pham Duy Khoa, Vu Vinh Huy Phat, Vo Thanh Viet, Le Duc |
| author_facet | Khanh, Pham Duy Khoa, Vu Vinh Huy Phat, Vo Thanh Viet, Le Duc |
| contents | In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of that type. The Lipschitz constants in both situations draw information solely from function values, and the global Lipschitz modulus is found when it exists. Some examples of classes of globally Lipschitz continuous convex functions beside the norms are also provided along with their global Lipschitz modulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lipschitz Modulus of Convex Functions via Function Values Khanh, Pham Duy Khoa, Vu Vinh Huy Phat, Vo Thanh Viet, Le Duc Optimization and Control 26A16, 52A41 In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of that type. The Lipschitz constants in both situations draw information solely from function values, and the global Lipschitz modulus is found when it exists. Some examples of classes of globally Lipschitz continuous convex functions beside the norms are also provided along with their global Lipschitz modulus. |
| title | Lipschitz Modulus of Convex Functions via Function Values |
| topic | Optimization and Control 26A16, 52A41 |
| url | https://arxiv.org/abs/2408.00586 |