New answers tagged convex-analysis
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Reference request for elementary convex geometry property
Indeed, this can be proved more simply, and in greater generality -- assuming only that the support of $P$ is contained in $C$ (rather than in $\mathcal X$).
Indeed, without loss of generality the ...
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Does approximately null gradient imply approximately global minimum for convex functions?
$\newcommand\Om\Omega\newcommand\R{\Bbb R}$The answer is no.
Indeed, for real $k>0$, let
$$G_k:=\{(x,y)\in\Bbb R^2\colon x>1,|y|<k\sqrt x\}. $$
For $(x,y)\in G_2$, let
$$f_0(x,y):=y^2/x-1.$$
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