Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification

TL;DR

This paper characterizes tilt stability of local minimizers in nonlinear programs under a relaxed constraint qualification, providing explicit formulas and extending previous results by relaxing key assumptions.

Contribution

It introduces new point-based characterizations of tilt stability under relaxed conditions and extends calculus rules for subgradient graphical derivatives.

Findings

Derived explicit formulas for tilt stability bounds.

Extended existing characterizations to relaxed constraint qualifications.

Provided examples illustrating the theoretical results.

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.