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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.

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Namaste, Shailesh, Daniel W. Farlow, user91500, Glorfindel
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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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