On the Topology of the Karush–Kuhn–Tucker Set under Mangasarian–Fromovitz Constraint Qualification
Harald Günzel · SIAM Journal on Control and Optimization · 1995
This paper deals with smooth optimization problems $\mathcal{P}$ in $\mathbb{R}^2 $ depending on parameter $y \in \mathbb{R}^2 $. The problem $\mathcal{P}(y)$ is defined by means of a finite number of equality and inequality constraints. We study the set $\Sigma _{KKT} $ of pairs $(x,t)$ such that x is a Karush–Kuhn–Tucker point of the problem $\mathcal{P}(y)$. Let $\Sigma $ denote the subset of $\Sigma _{KKT} $ at which the Mangasarian–Fromovitz constraint qualification is fulfilled. For problem data in general position we prove that $\Sigma $ is a topological manifold of dimension p.