get_curr_violations and violations computed based on eval_g and bounds do not agree #603
Description
I observed that in my application the violations as computed e.g. by get_curr_violations do not match those obtained "manually" when calling eval_g and subtracting / adding the upper / lower bound, respectively.
To check this, I resort to the hs071_cpp example and added these lines in the intermediate_callback function:
std::cout.precision(std::numeric_limits<Number>::max_digits10);
std::cout << std::endl << "Violations from get_curr_violations: \t"
<< constraint_violation[0] << " " << constraint_violation[1] << std::endl;
eval_g(4, x, true, 2, constraint_violation); // Compute violations based on current iterate x
std::cout << "Violations from eval_g: \t \t"
<< 25. - constraint_violation[0] << " " << constraint_violation[1] -40. << std::endl << std::endl;To keep the output clean, I out-commented the lines 414-455.
Furthermore, I added in finalize_solution the lines
std::cout << std::endl << "Final violations of the constraints:" << std::endl;
std::cout << "g(" << 0 << ") = " << 25. - g[0] << std::endl;
std::cout << "g(" << 1 << ") = " << g[1] - 40. << std::endl;This gives the output:
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit https://github.com/coin-or/Ipopt
******************************************************************************
This is Ipopt version 3.14.10, running with linear solver MUMPS 5.5.0.
Number of nonzeros in equality constraint Jacobian...: 4
Number of nonzeros in inequality constraint Jacobian.: 4
Number of nonzeros in Lagrangian Hessian.............: 10
Total number of variables............................: 4
variables with only lower bounds: 0
variables with lower and upper bounds: 4
variables with only upper bounds: 0
Total number of equality constraints.................: 1
Total number of inequality constraints...............: 1
inequality constraints with only lower bounds: 1
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
Violations from get_curr_violations: 0 11.243400939696002
Violations from eval_g: -0.096092162945630832 11.243400939696002
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
Violations from get_curr_violations: 0 0.74894595468575176
Violations from eval_g: -0.20860234632937491 0.74894595468575176
1 1.7410406e+01 7.49e-01 2.25e+01 -0.3 7.97e-01 - 3.19e-01 1.00e+00f 1
Violations from get_curr_violations: 0 0.0075231790452647829
Violations from eval_g: -1.0331199484597278 0.0075231790452647829
2 1.8001613e+01 7.52e-03 4.96e+00 -0.3 5.60e-02 2.0 9.97e-01 1.00e+00h 1
Violations from get_curr_violations: 0.03816758077581639 0.039953432860642124
Violations from eval_g: 0.038167830775815759 0.039953432860642124
3 1.7199482e+01 4.00e-02 4.24e-01 -1.0 9.91e-01 - 9.98e-01 1.00e+00f 1
Violations from get_curr_violations: 0.13720718679095611 0.15938033810270724
Violations from eval_g: 0.13720743679095548 0.15938033810270724
4 1.6940955e+01 1.59e-01 4.58e-02 -1.4 2.88e-01 - 9.66e-01 1.00e+00h 1
Violations from get_curr_violations: 0.021573856298374494 0.0061694408560200031
Violations from eval_g: 0.021574106298373863 0.0061694408560200031
5 1.7003411e+01 2.16e-02 8.42e-03 -2.9 7.03e-02 - 9.68e-01 1.00e+00h 1
Violations from get_curr_violations: 0.00020258544763862574 8.0748108949535435e-05
Violations from eval_g: 0.00020283544763799455 8.0748108949535435e-05
6 1.7013974e+01 2.03e-04 8.65e-05 -4.5 6.22e-03 - 1.00e+00 1.00e+00h 1
Violations from get_curr_violations: 2.7626678544834249e-07 7.1997845907390001e-08
Violations from eval_g: 5.2626678481715317e-07 7.1997845907390001e-08
7 1.7014017e+01 2.76e-07 2.18e-07 -10.3 1.43e-04 - 9.99e-01 1.00e+00h 1
Number of Iterations....: 7
(scaled) (unscaled)
Objective...............: 1.7014017031783709e+01 1.7014017031783709e+01
Dual infeasibility......: 2.1824331116938792e-07 2.1824331116938792e-07
Constraint violation....: 2.7626678544834249e-07 2.7626678544834249e-07
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 1.0473361552932239e-07 1.0473361552932239e-07
Overall NLP error.......: 2.7626678544834249e-07 2.7626678544834249e-07
Number of objective function evaluations = 8
Number of objective gradient evaluations = 8
Number of equality constraint evaluations = 8
Number of inequality constraint evaluations = 8
Number of equality constraint Jacobian evaluations = 8
Number of inequality constraint Jacobian evaluations = 8
Number of Lagrangian Hessian evaluations = 7
Total seconds in IPOPT = 0.005
EXIT: Optimal Solution Found.
Solution of the primal variables, x
x[0] = 1.0000000412793351
x[1] = 4.7429996061160633
x[2] = 3.8211500589803418
x[3] = 1.3794081892523982
Solution of the bound multipliers, z_L and z_U
z_L[0] = 1.0878716767473644
z_L[1] = 4.6358194761218199e-09
z_L[2] = 9.0874474076569869e-09
z_L[3] = 8.5559549728650972e-09
z_U[0] = 4.470027046608337e-09
z_U[1] = 4.0752309197030412e-07
z_U[2] = 1.1897911561120774e-08
z_U[3] = 6.398749117664807e-09
Objective value
f(x*) = 17.014017031783709
Final value of the constraints:
g(0) = 24.999999473733215
g(1) = 40.000000071997846
Final violations of the constraints:
g(0) = 5.2626678481715317e-07
g(1) = 7.1997845907390001e-08
*** The problem solved!
As you can see, the violations differ sometimes by more than machine epsilon and most importantly, the final solution does not bear the same violations as the iterate at which the optimizer stops!
As printed, I am using Ipopt 3.14.10 and MUMPS 5.5.0 and compiled with
g++ -std=c++11 -O0 -g -Wall -Wextra -Wpedantic `PKG_CONFIG_PATH=/usr/local/lib/pkgconfig: pkg-config --cflags ipopt` -c -o hs071_main.o hs071_main.cpp
g++ -std=c++11 -O0 -g -Wall -Wextra -Wpedantic -o hs071_nlp.exe hs071_nlp.o hs071_main.o `PKG_CONFIG_PATH=/usr/local/lib/pkgconfig: pkg-config --libs ipopt`
Is this reproducable?