ipopt_trace

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Description of Ipopt Tracing Output

Discussion

The following is a description, by column name, of the output for each iteration when its print_level option is 5 . This information comes from the ipopt output documentation.

iter

The current iteration count. This includes regular iterations and iterations during the restoration phase. If the algorithm is in the restoration phase, the letter r will be appended to the iteration number.

objective

The unscaled objective value at the current point. During the restoration phase, this value remains the unscaled objective value for the original problem.

inf_pr

The unscaled constraint violation at the current point. This quantity is the infinity-norm (max) of the (unscaled) constraint violation for \(g(x)\) in the Ipopt documentation. During the restoration phase, this value remains the constraint violation of the original problem at the current point. The option inf_pr_output can be used to switch to the printing of a different quantity.

inf_du

The scaled dual infeasibility at the current point. This quantity measure the infinity-norm (max) of the internal dual infeasibility, i.e, the derivative of the lagragian with respect to the primal variables

\[\nabla f(x) \nabla c(x) \lambda - z\]

where \(z\) are the lagrange multipliers for the box constraints and \(c(x)\) are the nonlinear equality constraints (inequality constraints are reformulated using slack variables and problem scaling). During the restoration phase, this is the value of the dual infeasibility for the restoration phase problem.

lg(mu)

\(\log_{10}\) of the value of the barrier parameter \(\mu\).

||d||

The infinity norm (max) of the primal step (for the original variables \(x\) and the internal slack variables \(s\)). During the restoration phase, this value includes the values of additional variables that capture the violation in \(c(x) = 0\).

lg(rg)

\(\log_{10}\) of the value of the regularization term for the Hessian of the Lagrangian in the augmented system. A dash (-) indicates that no regularization was done.

alpha_du

The step size for the dual variables for the box constraints in the equality constrained formulation; i.e., \(z\).

alpha_pr

The step size for the primal variables \(x\) and \(\lambda\) in the equality constrained formulation. The number is usually followed by a character for additional diagnostic information regarding the step acceptance criterion.

ls

The number of backtracking line search steps (does not include second-order correction steps).

Reference

A. Wachter and L. T. Biegler., On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Mathematical Programming, 106(1):25-57, 2006.