Ipopt输出的含义

https://coin-or.github.io/Ipopt/OUTPUT.html

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优化过程中的输出

This pages describes the standard Ipopt console output with the default setting for option print_level. The output is designed to provide a quick summary of each iteration as Ipopt solves the problem.

Before Ipopt starts to solve the problem, it displays the problem statistics (number of nonzero-elements in the matrices, number of variables, etc.). Note that if you have fixed variables (both upper and lower bounds are equal), Ipopt may remove these variables from the problem internally and not include them in the problem statistics.

Following the problem statistics, Ipopt will begin to solve the problem and you will see output resembling the following,

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  1.6109693e+01 1.12e+01 5.28e-01   0.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  1.8029749e+01 9.90e-01 6.62e+01   0.1 2.05e+00    -  2.14e-01 1.00e+00f  1
   2  1.8719906e+01 1.25e-02 9.04e+00  -2.2 5.94e-02   2.0 8.04e-01 1.00e+00h  1

and the columns of output are defined as,

1. 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.

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

3. inf_pr: The unscaled constraint violation at the current point. This quantity is the infinity-norm (max) of the (unscaled) constraints ( gL≤g(x)≤gU in (NLP)). 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.

4. inf_du: The scaled dual infeasibility at the current point. This quantity measure the infinity-norm (max) of the internal dual infeasibility, Eq. (4a) in the implementation paper [12], including inequality constraints reformulated using slack variables and problem scaling. During the restoration phase, this is the value of the dual infeasibility for the restoration phase problem.

5. lg(mu): log10 of the value of the barrier parameter μ.
   ||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, p and n (see Eq. (30) in [12]).

6. lg(rg): log10 of the value of the regularization term for the Hessian of the Lagrangian in the augmented system ( δw in Eq. (26) and Section 3.1 in [12]). A dash ("-") indicates that no regularization was done.

7. alpha_du: The stepsize for the dual variables ( αzk in Eq. (14c) in [12]).

8. alpha_pr: The stepsize for the primal variables ( αk in Eq. (14a) in [12]). The number is usually followed by a character for additional diagnostic information regarding the step acceptance criterion:
   

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

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返回值的含义

Note that the step acceptance mechanisms in Ipopt consider the barrier objective function (Eq (3a) in [12]) which is usually different from the value reported in the objective column. Similarly, for the purposes of the step acceptance, the constraint violation is measured for the internal problem formulation, which includes slack variables for inequality constraints and potentially scaling of the constraint functions. This value, too, is usually different from the value reported in inf_pr. As a consequence, a new iterate might have worse values both for the objective function and the constraint violation as reported in the iteration output, seemingly contradicting globalization procedure.

When the algorithm terminates, Ipopt will output a message to the screen based on the return status of the call to Optimize. The following is a list of the possible return codes, their corresponding output message to the console, and a brief description.

Solve_Succeeded:

Console Message: EXIT: Optimal Solution Found.

This message indicates that Ipopt found a (locally) optimal point within the desired tolerances.

Solved_To_Acceptable_Level:

Console Message: EXIT: Solved To Acceptable Level.

This indicates that the algorithm did not converge to the “desired” tolerances, but that it was able to obtain a point satisfying the “acceptable” tolerance level as specified by the acceptable_tol options. This may happen if the desired tolera