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The standard definition of strong convexity with a constant $m>0$ would read as follows: for $t \in [0,1]$, $$ f(tx+(1-t)y) \leq t f(x) + (1-t) f(y) - mt(1-t) \left \| x-y \right \|^2.$$ Now, there is a famous theorem that says that a function $f$ is strongly convex with constant $m>0$ if and only if the function $$g(x)=f(x)-m\left \|...

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