How to solve the following problem?

[Mark_L_Stone]

Minimize log(1+1/x) where 0<x<inf

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 q…