The concept of strong convexity extends and parametrizes the notion of strict convexity. A strongly convex function is also strictly convex, but not vice versa.
AIntuitively, a strongly-convex function is a function that grows as fast as a quadratic function.<ref>{{Cite web |title=Strong convexity · Xingyu Zhou's blog |url=https://xingyuzhou.org/blog/notes/strong-convexity |access-date=2023-09-27 |website=xingyuzhou.org}}</ref> Formally, a differentiable function <math>f</math> is called strongly convex with parameter <math>m > 0</math> if the following inequality holds for all points <math>x, y</math> in its ___domain:<ref name="bertsekas">{{cite book|page=[https://archive.org/details/convexanalysisop00bert_476/page/n87 72]|title=Convex Analysis and Optimization|url=https://archive.org/details/convexanalysisop00bert_476|url-access=limited|author=Dimitri Bertsekas| others= Contributors: Angelia Nedic and Asuman E. Ozdaglar|publisher=Athena Scientific|year=2003|isbn=9781886529458}}</ref><math display=block>(\nabla f(x) - \nabla f(y) )^T (x-y) \ge m \|x-y\|_2^2 </math>
