The problem is described as

\begin{array}{ll}

\text{minimize} & t \\

\text{subject to} & \tau+\rho*u+u*exp{\frac{-x^T*\xi-t-\tau}{u}}-u \leq \lambda \\

& u \geq 0

\end{array}

where \rho, \xi and \lambda are given parameters,x, t, u, \tau are variables to be solved.

Can this problem be solved by CVX?

How to express the constraints in CVX if it could be solved?

Thank you very much!