How to write expression like x*e^(y/x) in CVX?

1

Hello, I have a expression t_1*cp.exp(l_1a / t_1), where t_1 and l_1a are variables。 This function is the perspective of e^(l_1a), so it should be convex. However my cvx report an error saying this is not DCP。 How can I formulate this function？Kindly give the guidance. Thank you.

2

Use the exponential cone constraint (exp_cone in the CVX Users’ Guide), implemented as follows for x*exp(y/x) <= z

{y,x,z} == exponential(1)
which also enforces x > 0.

Then use z in place of x*exp(y/x)

3

This method works perfectly! Thank you very much for your suggestions.