On the uniform convexity of the squared distance
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918243683270656 |
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| author | Sipos, Andrei |
| author_facet | Sipos, Andrei |
| contents | In 1983, Zălinescu showed that the squared norm of a uniformly convex normed space is uniformly convex on bounded subsets. We extend this result to the metric setting of uniformly convex hyperbolic spaces. We derive applications to the convergence of shadow sequences and to proximal minimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the uniform convexity of the squared distance Sipos, Andrei Metric Geometry Optimization and Control 51F99, 52A55, 53C23 In 1983, Zălinescu showed that the squared norm of a uniformly convex normed space is uniformly convex on bounded subsets. We extend this result to the metric setting of uniformly convex hyperbolic spaces. We derive applications to the convergence of shadow sequences and to proximal minimization. |
| title | On the uniform convexity of the squared distance |
| topic | Metric Geometry Optimization and Control 51F99, 52A55, 53C23 |
| url | https://arxiv.org/abs/2503.03442 |