How to formulate u*exp(x/u) in cvx

1

I do not known how to formulate the following constraint in CVX
min t
s.t. \tau+ru+u\sum_{i=1}^N [exp(s_i/u)-1] leq \lambda,
s_i = (max_{k=1,2,3} a_k*(-x’*\xi^{i}-t)+b_k)-\tau,
u \geq 0,
x \geq 0,
\sum_i^n x_i = 1,

where x, t, \tau, u and s are decision variables. In the first constraint, u*exp(s_i/u) is actually a joint convex in s_i and u, but I have not found a proper way to formulate this constraint in CVX and made it implementable.

Many thanks.

2

Use exponential cone, per Exponential perspective function on CVX or Solve optimization problems of exp function

Did you forget the advice you got in How to express the special convex constraint in CVX? ?

3

Dear Mark,

Thanks for your quick response and kind remind. I indeed forgot what you suggested.

I will have a try.