New posts in Convex Analysis

How to show $f(z) = \sum_{j=1}^m \min_{\ell = 1, \cdots, q}\| x^j - z^\ell \|$ is NOT convex on $\mathbb{R}^n \times \cdots \times \mathbb{R}^n$

What is the convex hull of $\text{conv}(u_1,u_2,\cdots,u_p)+\text{conv}(v_1,v_2,\cdots,v_s)$?

Prove that $\Vert\cdot \Vert^2:X\to \Bbb{R},$ where $X$ is a vector space, is convex

Is a convex function always continuous?

When does Brunn-Minkowski inequatily $(m(A+B))^{1/d} \geqslant (m(A))^{1/d} + (m(B))^{1/d}$ become equality?

Why is the conjugate of a function always convex?

Set of symmetric positive semidefinite matrices is closed.

Does the domain of integration have to be convex?

Convex + Monotone =? Convex

Continuity of support functionals