A note on the weak Arrow-Hurwicz-Uzawa constraint qualification (Q1102195)

The following nonlinear programming problem is considered: \[ (NLP)\text{Maximize }f(x)\quad s.t.\quad x\in X\equiv \{x\in R^ n| g(x)\leq 0\}, \] where \(f: R^ n\to R\) and \(g: R^ n\to R^ m\) are differentiable functions. The concept of the weak Arrow-Hurwicz-Uzawa constraint qualification for the problem (NLP) is introduced. A necessary condition for this constraint qualification is derived.