I am looking for an example of a locally optimal point of the nonlinear program: $$\{ \min f(x) , g_i(x) \geq 0 \}$$ that does not have a singleton feasibility set.
e.g. not the example of $\{ \min x, x^2\leq 0 \} $ found here where the feasibility set is just $\{0\}$.