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arXiv · 2511.11384

On Characterizations of $\sigma$-Quasiconvexity

Nguyen Xuan Duy Bao·Nguyen Mau Nam
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Abstract

We revisit classical gradient characterizations of quasiconvexity and provide corrected proofs that close gaps in earlier arguments. For the differentiable case of $\sigma$-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.

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Nguyen Xuan Duy Bao, Nguyen Mau Nam. 2025-11-14. On Characterizations of $\sigma$-Quasiconvexity. https://arxiv.org/abs/2511.11384

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