# Tagged Questions

Convex analysis is the study of properties of convex sets and convex functions. For questions about optimization of convex functions over convex sets, please use the (convex-optimization) tag.

257 views

175 views

34 views

### Show that F can have at most two fixed points

Consider a function $F:\mathbb{R}^n\to\mathbb{R}^n$, where $F=(F_1,...,F_n)$. Suppose that $F$ is strictly quasi-concave, and that for all $i=1,...,n$ the function $F_i:\mathbb{R}^n\to\mathbb{R}$ is ...
30 views

### Differentiability of the composition of a Lipschitz, convex function and a power function

$f:\mathbb{R}^n\rightarrow \mathbb{R}$ is a positive, convex and Lipschitz function. Is the fuction $|f|^{2+\alpha}$, $\alpha>0$, twice continuously differentiable? How to prove it, or there is ...
Let $f: \mathbb R \rightarrow \mathbb [0, \infty)$ be a convex function. If $f$ is twice-differentiable, then $$(f^2)'' = (2ff')' = 2(f')^2 + 2f f'',$$ which is $\geq 0$ since $f, f'' \geq 0.$ But ...