{"ID":2841773,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11384","arxiv_id":"2511.11384","title":"On Characterizations of $σ$-Quasiconvexity","abstract":"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.","short_abstract":"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 lite...","url_abs":"https://arxiv.org/abs/2511.11384","url_pdf":"https://arxiv.org/pdf/2511.11384v2","authors":"[\"Nguyen Xuan Duy Bao\",\"Nguyen Mau Nam\"]","published":"2025-11-14T15:12:01Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}