# Is there any analytical/closed form solution of this problem? [closed]

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, GlorfindelJul 1 '17 at 9:30

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