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arXiv · 2408.00586

Lipschitz Modulus of Convex Functions via Function Values

Pham Duy Khanh·Vu Vinh Huy Khoa·Vo Thanh Phat·Le Duc Viet
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Abstract

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.

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Pham Duy Khanh, Vu Vinh Huy Khoa, Vo Thanh Phat, Le Duc Viet. 2024-08-01. Lipschitz Modulus of Convex Functions via Function Values. https://arxiv.org/abs/2408.00586

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