On Characterizations of $σ$-Quasiconvexity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917104795516928 |
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| author | Bao, Nguyen Xuan Duy Nam, Nguyen Mau |
| author_facet | Bao, Nguyen Xuan Duy Nam, Nguyen Mau |
| contents | We revisit classical gradient characterizations of quasiconvexity and provide corrected proofs that close gaps in earlier arguments. For the differentiable case of $σ$-quasiconvexity, we establish the full equivalence between several first-order conditions, resolving a remaining implication left open in the recent literature. Our approach yields a concise, self-contained proof of a classical characterization originally stated in the 1970s and sharpens the first-order theory for strong quasiconvexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Characterizations of $σ$-Quasiconvexity Bao, Nguyen Xuan Duy Nam, Nguyen Mau Optimization and Control 49J52, 49J53, 90C26, 26B25, 49K35 We revisit classical gradient characterizations of quasiconvexity and provide corrected proofs that close gaps in earlier arguments. For the differentiable case of $σ$-quasiconvexity, we establish the full equivalence between several first-order conditions, resolving a remaining implication left open in the recent literature. Our approach yields a concise, self-contained proof of a classical characterization originally stated in the 1970s and sharpens the first-order theory for strong quasiconvexity. |
| title | On Characterizations of $σ$-Quasiconvexity |
| topic | Optimization and Control 49J52, 49J53, 90C26, 26B25, 49K35 |
| url | https://arxiv.org/abs/2511.11384 |