# Strongly convex optimization error bounds

Suppose I want to minimize a function $$G(f)$$ using first order strongly convex methods and I get a solution $$f^*$$, where we restrict our solution set to strongly convex $$f$$. Now let $$f_0$$ be the theoretical minimizer for $$G(f)$$, not necessarily strongly convex.

Are there results out there that discuss how to bound $$G(f^*)-G(f_0)$$? We can assume our functions are smooth, but mainly I just want to know if there are any results out there.