However, in Writing x*log(1+x/y) ,the wizard of conic reformulation,@Michal_Adamaszek
produced the result
x*log(1+x/y) = rel_entr(x+y,y) + rel_entr(y,x+y)
Setting x = 1, then Interchanging the roles of x and y so as to match the problem in this thread, results in
log(1 + 1/x) = rel_entr(x,x+1) + rel_entr(x+1,x)
The RHS is accepted by CVX, and as a bonus, is already in a form needed by CVXQUAD. It executes without error.
And you can see how to formulate the matrix analog using CVXQUAD’s quantum_rel_entr at Perspective of log det function, and CVX formulations of related log det problems using Quantum Relative Entropy from CVXQUAD .