The local minimality of differentiable functions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918339559817216 |
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| author | Pham, Tien-Son |
| author_facet | Pham, Tien-Son |
| contents | In this paper we present necessary and sufficient conditions (in terms of Łojasiewicz inequalities) for the stability of local minimum points in smooth unconstrained optimization. In particular, we derive a sufficient condition for which the local minimum property of a given function is determined by its Taylor polynomial of a certain degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The local minimality of differentiable functions Pham, Tien-Son Optimization and Control 49K40, 90C30, 58K40 In this paper we present necessary and sufficient conditions (in terms of Łojasiewicz inequalities) for the stability of local minimum points in smooth unconstrained optimization. In particular, we derive a sufficient condition for which the local minimum property of a given function is determined by its Taylor polynomial of a certain degree. |
| title | The local minimality of differentiable functions |
| topic | Optimization and Control 49K40, 90C30, 58K40 |
| url | https://arxiv.org/abs/2602.13965 |