[Scip] SCIP behavior in nonlinear vs linear cases

[Ahmad Moradi]

Dear all,

I am working on a network design problem with concave cost function and
linear constraints. I implemented the problem in the following two forms

1. I directly added the concave cost objective function through expression
trees as nonlinear constraints. lets call this case "dynamic approximation".

2. I approximated the objective function with piecewise linear functions
(with fixed number of breakpoints) and then I have given the resulting MILP
to SCIP. lets call this case "static approximation".

I know that SCIP in dynamic case, will convexify the feasible region by
linearizing the nonlinear constraint (uses only two breakpoints and makes
the linearization by replacing a simple secant instead of the nonlinear
constraint ).

Now, I want to know, what is essentially the different between
SCIP's behavior on this two cases?

bests, Ahmad
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