In the Nonlinear programming textbook (Bazaraa et al.), the Theorem 4.2.16 (p. 195) states that, if $y$ is a KKT solution, and the objective $f$ is pseudoconvex at $y$, and the constraints $g_k$ are differentiable and quasiconvex at $y$, then $y$ is a global minimum of the constrained problem.
I need the following extended result that, if $f$ is strictly pseudoconvex at $y$, then $y$ is the unique global minimum. It's kind-of straightforward from the former theorem, but not mentioned in the textbook, and I cannot find it anywhere else. I'd rather not reinvent the wheel if there is a reference for this. Maybe someone here can point it to me?
Thanks