Minimize $\|C-C_0\|_F^2$ s.t. $1 \geq C \geq 0$ and $C1=1$ and $C^T 1=1$ and $C \in \mathbb{R}^{n \times n}$. Basically, I need an Euclidean Projection of a matrix on the doubly stochastic matrix. I have heard of Sinkhorn's algorithm but it minimizes the KL divergence rather.


closed as off-topic by Namaste, Shailesh, Daniel W. Farlow, user91500, Glorfindel Jul 1 '17 at 9:30

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  • $\begingroup$ Since you mention Sinkhorn's algorithm I'll point out that your problem is just a quadratic program in the entries of $C$. $\endgroup$ – Rahul Jun 29 '17 at 2:34
  • $\begingroup$ Quadratic Programming is iterative. I am looking for a closed form solution. $\endgroup$ – Buna Jun 29 '17 at 2:54

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