[Ipopt] A question about precision
Stefan Vigerske
stefan at math.hu-berlin.de
Tue Oct 29 06:33:00 EDT 2013
Hi,
the solution seems to be well within tolerances. 5e-5 is a feasible
value for the variables and 2e-9 is within optimality tolerance (1e-8) of 0.
Keep in mind that Ipopt is an **interior point** solver.
Stefan
On 10/29/2013 10:27 AM, darknesswind wrote:
> Hello! We just used very general example, but without the right result.
> How can we improve it?
>
> #Define variables, with bounds
> var x1 >= 0;
> var x2 >= 0;
>
> #objective function
> minimize objf: x1 * x2;
>
> #constaints
> NONE
>
> Normally, the objective value should equel to 0, because both of two variables can equal to 0.
> But we observed that the minimize variable value only get to 0.000050405560745489 in function eval_f(...),
> and the objective value just is 2.54072E-09.
>
> #Here is our relative option setting list
> List of options:
>
> Name Value # times used
> accept_every_trial_step = no 1
> acceptable_compl_inf_tol = 1e-006 1
> acceptable_constr_viol_tol = 1e-006 1
> acceptable_obj_change_tol = 1e-020 1
> acceptable_tol = 0.0001 1
> bound_mult_init_method = mu-based 1
> bound_relax_factor = 0 2
> compl_inf_tol = 1e-008 2
> constr_viol_tol = 1e-008 2
> dual_inf_tol = 1e-008 1
> file_print_level = 12 1
> hessian_approximation = limited-memory 4
> max_cpu_time = 1.79769e+308 1
> max_iter = 2147483647 1
> max_soc = 4 1
> mu_max = 1e+020 1
> mu_max_fact = 1e+008 1
> mu_min = 1e-020 1
> mu_oracle = quality-function 2
> mu_strategy = adaptive 2
> nlp_lower_bound_inf = -2e+024 1
> nlp_scaling_method = gradient-based 1
> nlp_upper_bound_inf = 2e+024 1
> obj_scaling_factor = 1 1
> output_file = ipopt.out 1
> tol = 1e-006 2
> watchdog_shortened_iter_trigger = 10 1
> watchdog_trial_iter_max = 3 1
>
> ########################################
> The output with default level is here:
>
> This is Ipopt version 3.11.1, running with linear solver mumps.
>
> Number of nonzeros in equality constraint Jacobian...: 0
> Number of nonzeros in inequality constraint Jacobian.: 0
> Number of nonzeros in Lagrangian Hessian.............: 0
>
> Total number of variables............................: 2
> variables with only lower bounds: 2
> variables with lower and upper bounds: 0
> variables with only upper bounds: 0
> Total number of equality constraints.................: 0
> Total number of inequality constraints...............: 0
> inequality constraints with only lower bounds: 0
> inequality constraints with lower and upper bounds: 0
> inequality constraints with only upper bounds: 0
>
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
> 0 1.0000000e-004 0.00e+000 9.99e+000 0.0 0.00e+000 - 0.00e+000 0.00e+000 0
> 1 1.0224810e-002 0.00e+000 9.12e-006 -0.0 9.11e-002 - 1.00e+000 1.00e+000f 1
> 2 8.2828361e-003 0.00e+000 8.18e-008 -2.1 1.01e-002 - 1.00e+000 1.00e+000f 1
> 3 2.4571876e-003 0.00e+000 7.40e-009 -3.1 4.14e-002 - 1.00e+000 1.00e+000f 1
> 4 6.2440136e-004 0.00e+000 2.01e-010 -4.7 2.46e-002 - 1.00e+000 1.00e+000f 1
> 5 1.6632570e-004 0.00e+000 2.01e-010 -4.7 1.21e-002 - 1.00e+000 1.00e+000f 1
> 6 4.1626583e-005 0.00e+000 9.03e-013 -7.0 6.44e-003 - 1.00e+000 1.00e+000f 1
> 7 1.0406667e-005 0.00e+000 4.14e-016 -10.4 3.23e-003 - 1.00e+000 1.00e+000f 1
> 8 2.6016718e-006 0.00e+000 1.06e-016 -11.0 1.61e-003 - 1.00e+000 1.00e+000f 1
> 9 6.5041926e-007 0.00e+000 2.65e-017 -11.6 8.06e-004 - 1.00e+000 1.00e+000f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
> 10 1.6260514e-007 0.00e+000 6.99e-018 -12.2 4.03e-004 - 1.00e+000 1.00e+000f 1
> 11 4.0651366e-008 0.00e+000 1.68e-018 -12.8 2.02e-004 - 1.00e+000 1.00e+000f 1
> 12 1.0162862e-008 0.00e+000 7.18e-019 -13.4 1.01e-004 - 1.00e+000 1.00e+000f 1
> 13 2.5407206e-009 0.00e+000 8.13e-020 -14.0 5.04e-005 - 1.00e+000 1.00e+000f 1
>
> Number of Iterations....: 13
>
> (scaled) (unscaled)
> Objective...............: 2.5407205540671768e-009 2.5407205540671768e-009
> Dual infeasibility......: 8.1315162936412833e-020 8.1315162936412833e-020
> Constraint violation....: 0.0000000000000000e+000 0.0000000000000000e+000
> Complementarity.........: 2.5407205540671810e-009 2.5407205540671810e-009
> Overall NLP error.......: 2.5407205540671810e-009 2.5407205540671810e-009
>
>
> Number of objective function evaluations = 14
> Number of objective gradient evaluations = 14
> Number of equality constraint evaluations = 0
> Number of inequality constraint evaluations = 0
> Number of equality constraint Jacobian evaluations = 0
> Number of inequality constraint Jacobian evaluations = 0
> Number of Lagrangian Hessian evaluations = 0
> Total CPU secs in IPOPT (w/o function evaluations) = 0.492
> Total CPU secs in NLP function evaluations = 0.056
>
> EXIT: Optimal Solution Found.
>
> #########################
> We will be appreciative of your answer.
>
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