All Questions

Let $X$ and $Y$ be metric spaces, and let $c:X\times Y\rightarrow \mathbb{R}$ be a nonnegative function which we refer to as a cost. For any $\phi:X\rightarrow \mathbb{R}$ and $\psi:Y\rightarrow \...

We say $(f_1,f_2,\dotsc,f_N)$ is a convex conjugate if for any $i=1,2,\dotsc,N$ and any $x_i\in\Bbb R^d$, we have: $$f_i(x_i)=\sup\left\{\sum_{k=1}^{N}\sum_{j=k+1}^N x_k x_j - \sum_{j=1,j\neq i}^N f_j(...