# On Constraint Qualifications of a Nonconvex Inequality

## TL;DR

This paper investigates various constraint qualifications for nonconvex inequalities using generalized normal cones and subdifferentials, extending classical convex results to broader nonconvex settings.

## Contribution

It introduces new constraint qualification conditions for nonconvex inequalities that generalize existing convex constraint qualifications.

## Key findings

- Several new constraint qualification conditions are proposed.
- These conditions unify and extend classical convex constraint qualifications.
- The results provide a framework for analyzing nonconvex inequalities.

## Abstract

In this paper, we study constraint qualifications for the nonconvex inequality defined by a proper lower semicontinuous function. These constraint qualifications involve the generalized construction of normal cones and subdifferentials. Several conditions for these constraint qualifications are also provided therein. When restricted to the convex inequality, these constraint qualifications reduce to basic constraint qualification (BCQ) and strong BCQ studied in [SIAM J. Optim., 14(2004), 757-772] and [Math. Oper. Res., 30 (2005), 956-965].