Is it true that every convex set of the Euclidean space is the sublevel set of some convex function?
60887
$d_A(x) = \inf_{a \in A} \|x-a\|$ is convex if and only if $A$ is convex
55866
Convex + Monotone =? Convex
113922
Proof that the intersection of any finite number of convex sets is a convex set
40438
Proving that closed (and open) balls are convex
36371
Exercise on convex functions
62135
Area under the graph of a convex function
110845
Convex Set with Empty Interior Lies in an Affine Set
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
87207
Prove that the support function of an arbitrary set $A\subset\mathbb R^n$ is convex
92029
Is this rational function convex?
123732
Proving that the maximum of two convex functions is also convex
90350
How can we replace $\sup$ with $\max$ in definition of subordinate norm for finite-dimensional vector space?
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
158399
Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
121095
Is convex hull of a finite set of points in $\mathbb R^2$ closed?
33527
Star convex set is simply connected.