SLSQP roundoff-limited with redundant equality constraints

[danlugli]

In preparation to the real problem I have, I am now trying SLSQP (NLopt 2.8.0 on windows) with a toy problem: find center and radius of a circumference given Ns samples on it. The samples are affected by some measurement error.
I minimize the sum of squared distances between the samples and their projections on the circumference, with the constraints that the projections must lie on the circumference (equality constraints).
I have therefore 3 + 2 Ns variables (2 coordinates of the center, radius, and 2 coordinates of each projection) and Ns constraints.
SLSQP works well and fast, even when I set (relatively) high measurement errors and start with a (relatively) bad initial approximation.
However my real problem has redundant constraints and it is not easy to discard some.
So I duplicated the constraints in the toy problem by adding each constraint twice.
In these conditions, SLSQP immediately gives up with a "nlopt roundoff-limited" exception.
Any suggestion on how to deal with a problem with redundant equality constraints?
Thank you in advance for any reply.

[danlugli]

I don't know the guts of SLSQP but I can imagine that, by adding each constraint twice, the jacobian of constraints, or any other matrix, will double its rows while keeping the same rank. If a linear system has to be solved with that matrix, it should be solvable anyway.

[jschueller]

could you provide the minimal code to reproduce it ?

[danlugli]

Here it is.
(The example works when REDUNDANT_CONSTRAINTS is 0, fails when it is 1)
TestNLopt2.zip

[danlugli]

It's a pity. Managing redundant constraints would be useful in several cases.