New posts in Convex Analysis

When is the Rayleigh quotient (spherically) convex?

On dual cones: $(K\cap L)^+\subseteq K^+ + L^+$

What is something (non-trivial) that can be done in Hilbert space but not Banach spaces for optimization problems?

Is $T(C) \subseteq R^m$ closed?

Image of $T:E \rightarrow \alpha E + (1-\alpha) E$ where $\alpha>1$.

How to show $\frac{1}{L}\|\nabla f(y)-\nabla f(x)\|_2^2 \leq \langle \nabla f(y) - \nabla f(x) ,y-x \rangle$ for strongly convex function?

$C_1$ and $C_2$ are non-crossing if they are translates of a convex disc

$\int_a^bf^2(x)\,dx\le \frac{2}{3}\int_a^bf(x)\,dx$ for a convex differentiable function

Why is a polar cone a closed set?

Prove that 0 is in the convex hull of points chosen from each orthant