{"ID":2894161,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12682","arxiv_id":"2507.12682","title":"On second-order weak sharp minima of general nonconvex set-constrained optimization problems","abstract":"This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer second-order tangent sets. Specifically, our findings eliminate the necessity of assuming convexity in the constraint set and/or the outer second-order tangent set, or the nonemptiness of the outer second-order tangent set. Furthermore, unlike traditional approaches, our sufficient conditions do not rely on strong assumptions such as the uniform second-order regularity of the constraint set and the property of uniform approximation of the critical cones.","short_abstract":"This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer s...","url_abs":"https://arxiv.org/abs/2507.12682","url_pdf":"https://arxiv.org/pdf/2507.12682v1","authors":"[\"Xiaoxiao Ma\",\"Wei Ouyang\",\"Jane Ye\",\"Binbin Zhang\"]","published":"2025-07-16T23:33:47Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}