Lambert Function


(Satyam Agarwal) #1

Lambert function (W(x)) satisfies the equation: x = W(x) exp(W(x)) for x ≥ −1/e. It is positive for x > 0 and is strictly concave.
How do I depict it as an objective in cvx?


(Mark L. Stone) #2

Concave? Yes.

Expressible in CVX? I very much doubt it. But if you find a way, please let us know.


(Erling D.Andersen) #3

See page 126 in

https://perso.uclouvain.be/francois.glineur/files/theses/Chares-PhD-thesis-2007.pdf

I am not sure CVX can handle the exponential cone needed.


(Michael C. Grant) #4

This is good! We do have exponential cone support, of course subject to our standard disclaimers about the successive approximation method.