Consider
a*log(a/(a+b)) + b*log(b/(a+b))
Rewrite this as
-a*log((a+b)/a) - b*log((a+b)/b)
which equals
-a*log(1+b/a) - b*log(1+a/b)
Please look at
help rel_entr
Now use rel_entr as described in Writing a constraint in DCP complient format
That results in
rel_entr(a,a+b) + rel_entr(b,a+b)
So I believe your expression can be created as
variable n(m+1)
yourexpression = sum(rel_entr(n,sum(n)-n))
Please check this to make sure I didn’t make any mistakes.