Abs(x)*exp(abs(x))

[zhang (zhangQK)]

What can do about abs(x)*exp(abs(x)) so that cvx can accept it?
Thank you.

[Michal_Adamaszek]

See

Interpolation error

If y\geq 0 then a model for t\geq y\exp(y) is essentially in https://docs.mosek.com/modeling-cookbook/expo.html#lambert-w-function, equation (5.10), up to renaming variables. Throwing in x we get the following model for t\geq y\exp(y/x), x,y\geq 0: t\geq y\exp(u/y) ux\geq y^2 The first one is an exponential cone the other is rotated quadratic. Now in general it should be OK to replace y with a positive z with z\geq |y| but frankly I haven’t checked all the correct monotonicity details. Eithe…

and around there.