Unable to implement this using entr() function. Any suggestions on how to implement this problem on cvx?

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07

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I believe the essence of the situation is your need to express the following construct in CVX:
x1*log(x1)+x2*log(x2) - (x1+x2)*log(x1+x2)

This can be re-written as

   x1*(log(x1) - log(x1+x2)) + x2*(log(x2) - log(x1+x2)) =
   x1*log(x1/(x1+x2)) + x2*log(x2/(x1+x2)) =
   rel_entr(x1,x1+x2) + rel_entr(x2,x1+x2)

I’ll let you extend this in the obvious way to your matrix variable and summation.

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Thank you for your quick response and your great help! I will try to use this now. Thanks again !