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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.

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  • $\begingroup$ It may be me, but I have serious troubles parsing this question. Is $G$ the function to be minimized over a set of functions $f$, so $G$ assigns a real value to a function, and for some reason you are interested in distinguishing between strongly convex or not functions $f$? $\endgroup$
    – Hannes
    Jan 14, 2021 at 12:05
  • $\begingroup$ Yes. That is correct. $\endgroup$
    – Kashif
    Jan 14, 2021 at 15:43

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