A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization

Understand

We study the set of continuous functions that admit no spurious local optima (i.e.

• local minima that are not global minima) which we term \textit{global functions}.
• They satisfy various powerful properties for analyzing nonconvex and nonsmooth optimization problems.
• For instance, they satisfy a theorem akin to the fundamental uniform limit theorem in the analysis regarding continuous functions.