My optimization program is
maximize(sum(x.*log( 1+1./x )))
subject to
x >= 0
sum(x) <= 1
and when running the code above, the following error occur
"cannot perform the operation: {positive constant}./{real affine}"
Does there exist some possible transformation that the problem can be dealt with cvx??
This seems highly nonconvex (especially given the affine constraints), in which case CVX cannot do much.
Note that
$$x\log(1+x^{-1})= x\log(x+1)-x\log x.$$
The function rel_entr implements
$$f(x,y) = x\log(x/y) = x\log x-x\log y.$$
Therefore, I believe that -rel_entr(x,x+1) will give you the function you need.
That said, I must point you to the warning given by CVX when attempting to solve models using logarithms, exponentials, and entropy functions, which is elaborated on here in the user gude.