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RobotLocomotion / drake

Model-based design and verification for robotics.
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IpoptSolver sets the sparsity parttern of the linear constraints. #21492

Closed hongkai-dai closed 1 month ago

hongkai-dai commented 1 month ago

Resolves #21485

cc @jorgenin

This change is Reviewable

hongkai-dai commented 1 month ago

@EricCousineau-TRI BTW, I just tested your example. The reason why Drake's IpoptSolver runs slower than Casadi is because Drake was using the default initial guess (the zero vector), as opposed to the initial guess set in the Casadi example.

I changed the code to use the same initial guess. Now Drake actually runs slightly faster than Casadi. Here is the output. Notice that in the first iteration Drake and Casadi evaluates the same objective

Starting test 2

List of user-set options:

                                    Name   Value                used
              acceptable_constr_viol_tol = 0.01                  yes
                          acceptable_tol = 1e-06                 yes
                         constr_viol_tol = 0.0001                yes
                   hessian_approximation = limited-memory        yes
                           linear_solver = mumps                 yes
                             print_level = 5                     yes
                 print_timing_statistics = no                    yes
                      print_user_options = yes                   yes
                                      sb = yes                   yes
                                     tol = 1e-08                 yes
This is Ipopt version drake_vendor, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...:      603
Number of nonzeros in inequality constraint Jacobian.:      400
Number of nonzeros in Lagrangian Hessian.............:        0

Total number of variables............................:      402
                     variables with only lower bounds:        1
                variables with lower and upper bounds:      201
                     variables with only upper bounds:        0
Total number of equality constraints.................:      202
Total number of inequality constraints...............:      200
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:      200

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  1.0001005e+02 1.00e-02 9.98e-01   0.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  1.0003383e+02 4.27e-03 6.77e-01  -4.3 9.29e-01    -  9.70e-01 5.73e-01h  1
   2  1.0003591e+02 1.88e-03 8.73e-01  -5.8 4.38e-01    -  9.85e-01 5.61e-01h  1
   3  1.0004087e+02 1.69e-02 1.60e-01  -3.5 2.44e-01    -  9.96e-01 8.98e-01h  1
   4  1.0001832e+02 1.53e-04 1.89e-03  -4.0 1.41e-01    -  9.85e-01 9.90e-01h  1
   5  1.0000105e+02 3.11e-18 2.70e-09  -5.3 6.83e-02    -  9.92e-01 1.00e+00h  1
   6  1.0000000e+02 3.33e-19 3.07e-11 -11.0 4.49e-03    -  9.91e-01 9.97e-01f  1
   7  9.9999999e+01 3.86e-22 1.44e-13 -11.0 5.41e-05    -  1.00e+00 1.00e+00f  1

Number of Iterations....: 7

                                   (scaled)                 (unscaled)
Objective...............:   9.9999998952050731e+01    9.9999998952050731e+01
Dual infeasibility......:   1.4359591999896980e-13    1.4359591999896980e-13
Constraint violation....:   3.8624003168684547e-22    3.8624003168684547e-22
Variable bound violation:   9.9975046968107693e-09    9.9975046968107693e-09
Complementarity.........:   1.0178693716247555e-11    1.0178693716247555e-11
Overall NLP error.......:   1.0178693716247555e-11    1.0178693716247555e-11

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             = 0
Total seconds in IPOPT                               = 0.030

EXIT: Optimal Solution Found.
-------------------------------------------
-------------------------------------------
-------------------------------------------
Casadi Sol

List of user-set options:

                                    Name   Value                used
              acceptable_constr_viol_tol = 0.01                  yes
                          acceptable_tol = 1e-06                 yes
                         constr_viol_tol = 0.0001                yes
                   hessian_approximation = limited-memory        yes
                           linear_solver = mumps                 yes
                             print_level = 5                     yes
                 print_timing_statistics = no                    yes
                      print_user_options = yes                   yes
                                      sb = yes                   yes
                                     tol = 1e-08                 yes
This is Ipopt version 3.14.11, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...:      603
Number of nonzeros in inequality constraint Jacobian.:      400
Number of nonzeros in Lagrangian Hessian.............:        0

Total number of variables............................:      402
                     variables with only lower bounds:        1
                variables with lower and upper bounds:      201
                     variables with only upper bounds:        0
Total number of equality constraints.................:      202
Total number of inequality constraints...............:      200
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:      200

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  1.0001005e+02 1.00e-02 9.98e-01   0.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  1.0003387e+02 4.26e-03 6.76e-01  -4.2 9.29e-01    -  9.70e-01 5.74e-01h  1
   2  1.0003594e+02 1.87e-03 8.71e-01  -5.7 4.38e-01    -  9.86e-01 5.62e-01h  1
   3  1.0001198e+02 1.01e-02 9.39e-02  -3.6 2.34e-01    -  9.94e-01 9.34e-01h  1
   4  1.0002131e+02 6.04e-04 3.54e-02  -4.0 1.13e-02    -  9.95e-01 9.49e-01h  1
   5  1.0001801e+02 2.44e-06 4.07e-03  -5.6 4.07e-03    -  1.00e+00 9.92e-01h  1
   6  1.0001347e+02 2.78e-18 4.76e-03  -7.2 4.76e-03    -  1.00e+00 1.00e+00f  1
   7  1.0001006e+02 2.41e-18 4.91e-03  -8.1 4.91e-03    -  1.00e+00 7.28e-01f  1
   8  1.0000789e+02 2.90e-18 4.28e-08  -5.8 8.62e+00    -  1.00e+00 3.50e-03f  1
   9  9.9999999e+01 2.88e-18 4.31e-10 -10.9 1.34e-02    -  9.89e-01 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  9.9999999e+01 1.85e-22 2.13e-14 -11.0 4.33e-06    -  1.00e+00 1.00e+00h  1

Number of Iterations....: 10

                                   (scaled)                 (unscaled)
Objective...............:   9.9999998952050007e+01    9.9999998952050007e+01
Dual infeasibility......:   2.1315227499335333e-14    2.1315227499335333e-14
Constraint violation....:   1.8528845721187820e-22    1.8528845721187820e-22
Variable bound violation:   9.9975031213371835e-09    9.9975031213371835e-09
Complementarity.........:   1.0006376209779095e-11    1.0006376209779095e-11
Overall NLP error.......:   1.0006376209779095e-11    1.0006376209779095e-11

Number of objective function evaluations             = 11
Number of objective gradient evaluations             = 11
Number of equality constraint evaluations            = 11
Number of inequality constraint evaluations          = 11
Number of equality constraint Jacobian evaluations   = 11
Number of inequality constraint Jacobian evaluations = 11
Number of Lagrangian Hessian evaluations             = 0
Total seconds in IPOPT                               = 0.084

EXIT: Optimal Solution Found.
      solver  :   t_proc      (avg)   t_wall      (avg)    n_eval
       nlp_f  | 208.00us ( 18.91us)  31.16us (  2.83us)        11
       nlp_g  | 701.00us ( 63.73us) 106.61us (  9.69us)        11
  nlp_grad_f  | 391.00us ( 32.58us)  53.57us (  4.46us)        12
   nlp_jac_g  | 824.00us ( 68.67us) 124.28us ( 10.36us)        12
       total  | 543.93ms (543.93ms)  87.33ms ( 87.33ms)         1
Solve time:  2.076539993286133
Solve time 2 :  0.030740976333618164
Casadi Solve Time: 0.08748602867126465
Controls norm:  1.358751404045516e-07
Integral norm:  4.4793890387626446e-08
Max norm:  6.991740519879386e-12
Controls norm casadi:  1.3579234259034422e-07
Integral norm casadi:  4.4805843778744453e-08
Max norm casadi:  7.005951374594588e-12

The difference in the computation is probably due to different ordering of the constraints.

EricCousineau-TRI commented 1 month ago

awesome, thanks! and ftr, it was not my example, but just taking @jorgenin's example and putting it into Drake for quick testing.