[Couenne] balanced branching strategy in couenne

[Pete Janes]

Hi Pietro,

I am looking at the procedure for the balanced branching strategy in Couenne.
I undertand that it computes the branching point which minimizes the differences
in the distance between LP1 and the primal function, and LP2 and the
primal function.
Where LP1 and LP2 are the two LP's to be generated by the hypothetical branch.

Looking at the code, it appears that this procedure assumes that the
primal function
is uniformly convex or concave - as the LP are taken to be the line
segment from
the two end points of the primal function. However, in Couenne,
functions such as
x^3 also uses the balanced branching strategy, and it has an inflection point.

Can this be problematic in some isolated cases? (I am currently
implementing a relaxation
for a univariate function that has one saddle point) Should I use a
simpler strategy just in
case?

Kind regards,

Pete