How to express a constraint in MOSEK

Question

I have the following constraint to be implemented in Mosek, where the unknown variable is x.

I'm trying to follow the discussion here. I could write the constraint as the intersection between 15 exponential cones and one half space. However, what is the best way to write the exponential cone in Mosek given that I have a linear combination of the elements of the unknown x?

Answer 1

In Fusion API you write the constraint t\geq exp(u) as

M.constraint(Expr.hstack(t, Expr.constTerm(1.0), u), Domain.inPExpCone())

and u can be an expression constructed in a more complicated way, say

y1 = Expr.sub(Expr.dot(c1, x), b1)
u = Expr.mul(r, y1)
....

and so on.