I am solving a convex problem using CVX, the code is

cvx_begin
variable T nonnegative
variable t nonnegative
minimize (t*(exp(d*inv_pos(t)-1) +inv_pos(T^2)
subject to
T >= c;
at +bT <=0;
cvx_end

a and b are constant, which is a randomly generated real number. c and d are pre-defined positive constants.
As I checked, the objective function is convex, yet I receive the consequence of

So unless you are missing a minus sign, the first term is concave and the 2nd term is convex. Therefore it is neither convex nor concave, and canâ€™t be formulated for CVX. If you are missing a minus sign in the first term, here you go.

EDIT; This answer is wrong because I misread the problem. See my post below.

As far as I know, the rel_entr is function related with log function.
However, my function is in the form of t*exp(1/t), which is convex.
Are you saying I should apply variable substitution?