[Ipopt] enforcing once a step size of alpha=1

[Martin Neuenhofen]

Hi all,

my problem has linear equality conditions and my problem is badly scaled. I
thought that ill scaling of linear equality constraints is not necessary to
be considered because it once solves the residual to zero and then does not
occur in the step size scaling any more, BUT however this only holds after
the residual of this equality has once reached zero.

Explanation:
Solve F(x)=0 with F = [A*x1-b ; G(x2)] for x = [x1;x2].
In this case the Newton Step is x = x - alpha * [invA, 0; 0, inv(DG)] *
[A*x1-b ; G(x2)] , where alpha is the step size. So when A*x1-b is not zero
yet the NLP is ill-scaled or the Hesse-approx bad, then the residual of
these equalities will slow down convergence *until* one step with alpha=1
is performed because afterwards A*x1-b=0 will always hold for all
subsequent steps.

Therefore, is there an option in ipopt such that I can once enforce in the
beginning a stepsize of alpha=1? If not, did someone have a similar issue
and found a work-around? I am afraid one cannot simply use an alpha=1 in a
hand-build feasibility Newton solver in advance of the first step because
of the inequality constraints.

Kind regards,
Martin
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