`x*log(1+x/(x+y))`

for x >= 0, y >= 0 is jointly convex in x and y.

Similarly to Xlog( 1+ Y/(X+Y) ): DCP rules, and build-in functions in cvx , we can derive that

`x*log(1+x/(x+y))`

can be represented as

`rel_entr(x+y,2*x+y) + rel_entr(2*x+y,x+y)`

`x*log(1+x/(x+y))`

for x >= 0, y >= 0 is jointly convex in x and y.

Similarly to Xlog( 1+ Y/(X+Y) ): DCP rules, and build-in functions in cvx , we can derive that

`x*log(1+x/(x+y))`

can be represented as

`rel_entr(x+y,2*x+y) + rel_entr(2*x+y,x+y)`

Perspective of log det function, and CVX formulations of related log det problems using Quantum Relative Entropy from CVXQUAD