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arXiv · 2508.06927

Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification

Nguyen Huy Chieu·Nguyen Thi Quynh Trang·Nguyen Thi Hai Yen
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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.

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Nguyen Huy Chieu, Nguyen Thi Quynh Trang, Nguyen Thi Hai Yen. 2025-08-09. Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification. https://arxiv.org/abs/2508.06927

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