Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification
Optimization and Control
2025-08-12 v1
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.
Keywords
Cite
@article{arxiv.2508.06927,
title = {Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification},
author = {Nguyen Huy Chieu and Nguyen Thi Quynh Trang and Nguyen Thi Hai Yen},
journal= {arXiv preprint arXiv:2508.06927},
year = {2025}
}