[SCIP] Nonlinear constraints / expression trees

[Johannes Thürauf]

Dear SCIP-Team,

I would really appreciate if you can help me by providing some information
about how Scip handles nonlinear constraints.

I want to implement an algorithm which computes a linearisation
(delta-method) and a relaxation of nonlinear constraints such as
exp(x)-y=0.
I have already understood that Scip uses Expression Trees to store the
representation of nonlinear constraints. Unfortunately I have never worked
with expression Trees before. So hopefully you can give me an advise where
I can find some information about how Scip works with expression trees.
Moreover Scip is doing a lot of "presolve" when reading the problem. For
example when I have the constraint exp(x)*ln(s)-y=0
Scip transforms this constraint to the following kind:
exp(x)-z=0 (1)
ln(s)-w=0  (2)
z*w-y=0    (3)
My question is will Scip always transform all nonlinear constraint this way?
So that you have always constraints with maximum one nonlinear term?
If this would be the case, there would be no need for me to transform the
nonlinear constraint to the following type: (one) nonlinearexpr - (one)
variable =0 such as (1) or product of vars - vars =0 such as (3).
Thank you very much

Yours sincerely,

Johannes Thürauf


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