[Ipopt] Derivative check program returns eps
Stefan Vigerske
stefan at math.hu-berlin.de
Mon Aug 20 08:58:49 EDT 2018
Hi,
I don't see "overflowed errors" or a crash in the log.
There is this "Using overestimation factor LiwFact = 2.000000e+00" line,
but that isn't an error. It just says that Ipopt will allocate more
memory than what is requested by the linear solver to be on the safe side.
The derivative test should use the user provided starting point as the
one that is perturbed.
Best,
Stefan
On 6/16/18 11:30 PM, Takafumi Usui wrote:
> Dear all,
>
> I am using IPOPT (3.12.9) from python via pyipopt to solve a stochastic optimization problem.
> I am struggling with a derivative check error, which do not show up when I solve a similar but even harder problem though.
>
> When I perform the IPOPT provided derivative check program, it returns eps, while my Jacobian shows different numbers.
>
> When I introduce an additional constraint, overflowed errors, which you can observe in my log file below, show up. Without this constraint, my Jacobian and the derivative check program return almost the same numbers.
> I also know that this constraint works correctly with harder examples.
>
> I guess that the derivative check program perturbates x to calculate numerically approximated derivatives but I am not sure from which point the program starts. Is it from user provided starting point?
>
> The derivative check program seems to crash in my example below. What kind of problems could induce these differences between the user and the IPOPT provided derivative checker?
>
> I know that this kind of issues are problem specific, but if someone has an idea or experience to solve this kind of problem, I would appreciate your help.
>
> Thank you in advance for your help and I hope to hear from you soon.
>
> Best regards,
>
> Takafumi
>
> *****************************************************************************
> List of options:
>
> Name Value # times used
> derivative_test = first-order 1
> derivative_test_print_all = yes 1
> hessian_approximation = limited-memory 7
> print_level = 7 2
>
> ******************************************************************************
> 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 http://projects.coin-or.org/Ipopt
> ******************************************************************************
>
> This is Ipopt version 3.12.9, running with linear solver ma27.
>
> Starting derivative checker for first derivatives.
>
> grad_f[ 0] = 0.0000000000000000e+00 ~ 0.0000000000000000e+00 [ 0.000e+00]
> * jac_g [ 0, 0] = 8.0112183553637806e-01 v ~ 3.9525251667299724e-313 [ 8.011e-01]
> * jac_g [ 1, 0] = -1.4579448759377556e-04 v ~ 2.3715151000379834e-314 [ 1.458e-04]
> * jac_g [ 2, 0] = 1.0000000161269895e+00 v ~ 2.3715151000379834e-314 [ 1.000e+00]
> * jac_g [ 3, 0] = 3.3598603899065438e+00 v ~ -4.7430302000759668e-314 [ 3.360e+00]
> jac_g [ 4, 0] = 0.0000000000000000e+00 v ~ 2.0157878350322859e-313 [2.016e-313]
> jac_g [ 5, 0] = 0.0000000000000000e+00 v ~ 5.9287877500949585e-314 [5.929e-314]
> * jac_g [ 6, 0] = -5.7511222451012145e-01 v ~ -2.3715151000379834e-314 [ 5.751e-01]
> grad_f[ 1] = 0.0000000000000000e+00 ~ 0.0000000000000000e+00 [ 0.000e+00]
> * jac_g [ 0, 1] = 2.6980906397966464e-01 v ~ 1.7214366718091040e-314 [ 2.698e-01]
> * jac_g [ 1, 1] = 1.8005731350356768e-01 v ~ 1.5492930037882820e-315 [ 1.801e-01]
> jac_g [ 2, 1] = 0.0000000000000000e+00 v ~ -1.0328620041724068e-315 [1.033e-315]
> jac_g [ 3, 1] = 0.0000000000000000e+00 v ~ -1.0328620041724068e-315 [1.033e-315]
> * jac_g [ 4, 1] = 1.0000000827403710e+00 v ~ 5.1643099961587518e-316 [ 1.000e+00]
> * jac_g [ 5, 1] = 5.6548944971090975e+00 v ~ 1.1361482031074506e-314 [ 5.655e+00]
> * jac_g [ 6, 1] = -9.8093595468640160e-01 v ~ 2.0657240083448136e-315 [ 9.809e-01]
> grad_f[ 2] = 0.0000000000000000e+00 ~ 0.0000000000000000e+00 [ 0.000e+00]
> * jac_g [ 0, 2] = 5.7511222451012145e-01 v ~ 4.6234271373410638e-314 [ 5.751e-01]
> * jac_g [ 1, 2] = 9.8093595468640160e-01 v ~ 2.7740562821081989e-314 [ 9.809e-01]
> jac_g [ 2, 2] = 0.0000000000000000e+00 v ~ 0.0000000000000000e+00 [ 0.000e+00]
> jac_g [ 3, 2] = 0.0000000000000000e+00 v ~ -1.3870281403130010e-315 [1.387e-315]
> jac_g [ 4, 2] = 0.0000000000000000e+00 v ~ -4.1610844258796594e-315 [4.161e-315]
> jac_g [ 5, 2] = 0.0000000000000000e+00 v ~ 8.3221688468186624e-315 [8.322e-315]
> * jac_g [ 6, 2] = 2.0003376732802280e-02 v ~ 9.7091969871316634e-315 [ 2.000e-02]
> grad_f[ 3] = 0.0000000000000000e+00 ~ 0.0000000000000000e+00 [ 0.000e+00]
> * jac_g [ 0, 3] = -1.0000000827403710e+00 v ~ 1.1763956867539469e-313 [ 1.000e+00]
> jac_g [ 1, 3] = 0.0000000000000000e+00 v ~ 1.4116748239268727e-314 [1.412e-314]
> jac_g [ 2, 3] = 0.0000000000000000e+00 v ~ 3.5291870585820176e-315 [3.529e-315]
> * jac_g [ 3, 3] = -3.1445930304130343e+00 v ~ 5.6466992962015564e-314 [ 3.145e+00]
> jac_g [ 4, 3] = 0.0000000000000000e+00 v ~ -3.5291870585820176e-315 [3.529e-315]
> jac_g [ 5, 3] = 0.0000000000000000e+00 v ~ 7.0583741221046916e-315 [7.058e-315]
> jac_g [ 6, 3] = 0.0000000000000000e+00 v ~ -3.1762683542060128e-314 [3.176e-314]
> grad_f[ 4] = 0.0000000000000000e+00 ~ 0.0000000000000000e+00 [ 0.000e+00]
> jac_g [ 0, 4] = 0.0000000000000000e+00 v ~ 6.9895653955592695e-314 [6.990e-314]
> * jac_g [ 1, 4] = -9.9999999392252903e-01 v ~ 0.0000000000000000e+00 [ 1.000e+00]
> jac_g [ 2, 4] = 0.0000000000000000e+00 v ~ 3.7743653137107000e-314 [3.774e-314]
> jac_g [ 3, 4] = 0.0000000000000000e+00 v ~ 0.0000000000000000e+00 [ 0.000e+00]
> jac_g [ 4, 4] = 0.0000000000000000e+00 v ~ 0.0000000000000000e+00 [ 0.000e+00]
> * jac_g [ 5, 4] = -3.1338184269813496e-01 v ~ 8.3874784754616284e-315 [ 3.134e-01]
> jac_g [ 6, 4] = 0.0000000000000000e+00 v ~ -4.1937392352604860e-315 [4.194e-315]
>
> Derivative checker detected 17 error(s).
>
> Number of nonzeros in equality constraint Jacobian...: 25
> Number of nonzeros in inequality constraint Jacobian.: 10
> Number of nonzeros in Lagrangian Hessian.............: 0
>
> Hessian approximation will be done in the space of all 5 x variables.
>
> Scaling parameter for objective function = 1.000000e+00
> objective scaling factor = 1
> No x scaling provided
> No c scaling provided
> No d scaling provided
> Moved initial values of x sufficiently inside the bounds.
> Moved initial values of s sufficiently inside the bounds.
> Total number of variables............................: 5
> variables with only lower bounds: 0
> variables with lower and upper bounds: 5
> variables with only upper bounds: 0
> Total number of equality constraints.................: 5
> Total number of inequality constraints...............: 2
> inequality constraints with only lower bounds: 2
> inequality constraints with lower and upper bounds: 0
> inequality constraints with only upper bounds: 0
>
> Convergence Check:
> overall_error = 5.1119232457805285e-313 IpData().tol() = 1.0000000000000000e-08
> dual_inf = 1.0000000000000000e+00 dual_inf_tol_ = 1.0000000000000001e+300
> constr_viol = 5.1119232457805285e-313 constr_viol_tol_ = 1.0000000000000000e-04
> compl_inf = 9.9990001010000000e+01 compl_inf_tol_ = 1.0000000000000001e+300
>
>
> **************************************************
> *** Summary of Iteration: 0:
> **************************************************
>
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
> 0 0.0000000e+00 5.11e-313 1.00e+00 0.0 0.00e+00 - 0.00e+00 0.00e+00 0 s
>
> **************************************************
> *** Beginning Iteration 0 from the following point:
> **************************************************
>
> Current barrier parameter mu = 1.0000000000000000e+00
> Current fraction-to-the-boundary parameter tau = 0.0000000000000000e+00
>
> ||curr_x||_inf = 2.3870770173449724e+01
> ||curr_s||_inf = 9.9999900000000003e-03
> ||curr_y_c||_inf = 0.0000000000000000e+00
> ||curr_y_d||_inf = 0.0000000000000000e+00
> ||curr_z_L||_inf = 1.0000000000000000e+00
> ||curr_z_U||_inf = 1.0000000000000000e+00
> ||curr_v_L||_inf = 1.0000000000000000e+00
> ||curr_v_U||_inf = 0.0000000000000000e+00
>
> No search direction has been computed yet.
>
>
> ***Current NLP Values for Iteration 0:
>
> (scaled) (unscaled)
> Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
> Dual infeasibility......: 1.0000000000000000e+00 1.0000000000000000e+00
> Constraint violation....: 5.1119232457805285e-313 5.1119232457805285e-313
> Complementarity.........: 9.9990001010000000e+01 9.9990001010000000e+01
> Overall NLP error.......: 5.1119232457805285e-313 9.9990001010000000e+01
>
>
>
> In Ma27TSolverInterface::InitializeStructure: Using overestimation factor LiwFact = 2.000000e+00
> Return values from MA27AD: IFLAG = 0, IERROR = 0
> Size of integer work space recommended by MA27 is 104
> Setting integer work space size to 520
> Size of doublespace recommended by MA27 is 148
> Setting double work space size to 740
> Return values from MA27BD: IFLAG = 0, IERROR = 0
> Number of doubles for MA27 to hold factorization (INFO(9)) = 71
> Number of integers for MA27 to hold factorization (INFO(10)) = 33
> Factorization successful.
>
> Number of Iterations....: 0
>
> (scaled) (unscaled)
> Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
> Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
> Constraint violation....: 5.1119232457805285e-313 5.1119232457805285e-313
> Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
> Overall NLP error.......: 5.1119232457805285e-313 5.1119232457805285e-313
>
>
> Number of objective function evaluations = 1
> Number of objective gradient evaluations = 1
> Number of equality constraint evaluations = 1
> Number of inequality constraint evaluations = 1
> Number of equality constraint Jacobian evaluations = 1
> Number of inequality constraint Jacobian evaluations = 1
> Number of Lagrangian Hessian evaluations = 0
> Total CPU secs in IPOPT (w/o function evaluations) = 0.009
> Total CPU secs in NLP function evaluations = 0.003
>
> EXIT: Optimal Solution Found.
>
>
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