On the convergence of critical points on real algebraic sets and applications to optimization

Saugata Basu, Ali Mohammad-Nezhad

Let $F\in \mathbb{R}[X_1,\dots ,X_n]$ and the zero set $V=\zero(\mathcal{P},\R^n)$, where $\mathcal{P}:=\{P_1,\dots ,P_s\}\subset \mathbb{R}[X_1,\dots ,X_n]$ is a finite set of polynomials. We i…