[Ipopt] Indefinite Hessian

Hans Pirnay hans.pirnay at rwth-aachen.de
Wed Feb 8 06:17:53 EST 2012

On Wed, Feb 8, 2012 at 10:44 AM, Altmannshofer, Simon
<simon.altmannshofer at tum.de> wrote:
> Hello,
> I am using IPOPT to solve the NLP arising in Nonlinear Model Predictive
> Control. IPOPT was compiled with MS Visual Studio 10 according to the
> documentation. In order to access IPOPT in MATLAB/Simulink the C Interface
> is used.
> At the starting point, the user-supplied hessian is indefinite (checked with
> MATLAB's chol(hessian)). According to the implementation IPOPT should add a
> multiple of the unity matrix to the indefinite hessian. Unfortunately this
> is not done and the objective function is only reduced slightly. See the
> output :

1. You don't necessarily need regularization just because the hessian
of the lagrangean is indefinite -> think linear programs.

2. The objective function value is not really informative here. Ipopt
tries to reduce the dual infeasibility first. From the output you can
see that Ipopt has not decreased mu yet - it is still at its starting
value 0.1. However, the iterates only converge to the solution for
mu->0. You simply need more iterations.

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