Subsections

Hessian Perturbation


max_hessian_perturbation:

Maximum value of regularization parameter for handling negative curvature.
In order to guarantee that the search directions are indeed proper descent directions, Ipopt requires that the inertia of the (augmented) linear system for the step computation has the correct number of negative and positive eigenvalues. The idea is that this guides the algorithm away from maximizers and makes Ipopt more likely converge to first order optimal points that are minimizers. If the inertia is not correct, a multiple of the identity matrix is added to the Hessian of the Lagrangian in the augmented system. This parameter gives the maximum value of the regularization parameter. If a regularization of that size is not enough, the algorithm skips this iteration and goes to the restoration phase. (This is delta_wmax in the implementation paper.) The valid range for this real option is $ 0 < {\tt max\_hessian\_perturbation } < {\tt +inf}$ and its default value is $ 1 \cdot 10^{+20}$.


min_hessian_perturbation:

Smallest perturbation of the Hessian block.
The size of the perturbation of the Hessian block is never selected smaller than this value, unless no perturbation is necessary. (This is delta_wmin in implementation paper.) The valid range for this real option is $ 0 \le {\tt min\_hessian\_perturbation } < {\tt +inf}$ and its default value is $ 1 \cdot 10^{-20}$.


first_hessian_perturbation:

Size of first x-s perturbation tried.
The first value tried for the x-s perturbation in the inertia correction scheme.(This is delta_0 in the implementation paper.) The valid range for this real option is $ 0 < {\tt first\_hessian\_perturbation } < {\tt +inf}$ and its default value is $ 0.0001$.


perturb_inc_fact_first:

Increase factor for x-s perturbation for very first perturbation.
The factor by which the perturbation is increased when a trial value was not sufficient - this value is used for the computation of the very first perturbation and allows a different value for for the first perturbation than that used for the remaining perturbations. (This is bar_kappa_w+ in the implementation paper.) The valid range for this real option is $ 1 < {\tt perturb\_inc\_fact\_first } < {\tt +inf}$ and its default value is $ 100$.


perturb_inc_fact:

Increase factor for x-s perturbation.
The factor by which the perturbation is increased when a trial value was not sufficient - this value is used for the computation of all perturbations except for the first. (This is kappa_w+ in the implementation paper.) The valid range for this real option is $ 1 < {\tt perturb\_inc\_fact } < {\tt +inf}$ and its default value is $ 8$.


perturb_dec_fact:

Decrease factor for x-s perturbation.
The factor by which the perturbation is decreased when a trial value is deduced from the size of the most recent successful perturbation. (This is kappa_w- in the implementation paper.) The valid range for this real option is $ 0 < {\tt perturb\_dec\_fact } < 1$ and its default value is $ 0.333333$.


jacobian_regularization_value:

Size of the regularization for rank-deficient constraint Jacobians.
(This is bar delta_c in the implementation paper.) The valid range for this real option is $ 0 \le {\tt jacobian\_regularization\_value } < {\tt +inf}$ and its default value is $ 1 \cdot 10^{-08}$.