{"ID":2884359,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.06927","arxiv_id":"2508.06927","title":"Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification","abstract":"This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus rules for subgradient graphical derivative, we obtain some pointbased characterizations of tilt-stable local minimizers along with an explicit formula for calculating the exact bound of tilt stability. These results extend the corresponding ones of H. Gfrerer and B.S.Mordukhovich [SIAM J. Optim. 25 (2015), 2081-2119] by relaxing the constraint qualification and removing the linear independence condition of gradients of equality constraint functions. Examples are provided illustrating our findings.","short_abstract":"This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus rules for subgradient graphical derivative, we obtain some pointbased characterizat...","url_abs":"https://arxiv.org/abs/2508.06927","url_pdf":"https://arxiv.org/pdf/2508.06927v1","authors":"[\"Nguyen Huy Chieu\",\"Nguyen Thi Quynh Trang\",\"Nguyen Thi Hai Yen\"]","published":"2025-08-09T10:46:44Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}