Ipopt Warm Start in CppAD

[Magic-wei]

Hi,

I'm currently using CppAD along with Ipopt for my MPC project and it works well. Next, I want to explore warm start settings of Ipopt in CppAD in order to reduce the computation time cost. However, I followed some blogs to try it out but got errors on my machine. Detailed information is given as follows. Can you offer some help?

Blogs & Docs I followed

• [Ipopt] How to warm start dual variables in IPOPT?
• Ipopt: Special Features - Warm-Starting Capabilities via AMPL
• Ipopt Options - Warm Start
• I also dived into the function CppAD::ipopt::solve and some CppAD header files, it looks like there is no support for Ipopt warm start settings (e.g. I can't find interface to tell the Ipopt solver about Lagrange multipliers zl, zu, lambda in the last run).

Basic information

• OS: Ubuntu 16.04.7 LTS (xenial)
• Kernel: 4.10.0-28-generic
• Ipopt version: 3.12.4 (running with linear solver mumps)
• CppAD version: 20180000.0

Run
run CppAD::Ipopt::solve twice, the only difference is options.

1. In the first run, the solver was running as usual and found optimal solution. Options are:

Integer print_level  6
Sparse  true        forward
Sparse  true        reverse
Numeric max_cpu_time          0.5
String print_user_options yes
String nlp_scaling_method none

2. In the second run, I set up Ipopt warm start options as follows and keep everything else the same as the first run. I got errors this time. Error information will be listed below.

Integer print_level  6
Sparse  true        forward
Sparse  true        reverse
Numeric max_cpu_time          0.5
String print_user_options yes
String nlp_scaling_method none
String warm_start_init_point   yes
Numeric warm_start_bound_frac   1e-16
Numeric warm_start_bound_push   1e-16
Numeric warm_start_mult_bound_push   1e-16
Numeric warm_start_slack_bound_frac   1e-16
Numeric warm_start_slack_bound_push   1e-16

Error information for the second run:

cppad-20180000.0 error from unknown source
Error detected by false result for
    init_z == false
at line 596 in the file 
    /usr/include/cppad/ipopt/solve_callback.hpp
motion_control_node: /usr/include/cppad/utility/error_handler.hpp:206: static void CppAD::ErrorHandler::Default(bool, int, const char*, const char*, const char*): Assertion `false' failed.

Detailed Information

=============== First Run ===============

List of user-set options:

                                    Name   Value                used
                            max_cpu_time = 0.5                   yes
                      nlp_scaling_method = none                  yes
                             print_level = 6                     yes
                      print_user_options = yes                   yes

List of options:

                                    Name   Value                # times used
                            max_cpu_time = 0.5                       1
                      nlp_scaling_method = none                      1
                             print_level = 6                         2
                      print_user_options = yes                       1

******************************************************************************
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 3.12.4, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian...:      191
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:       89

objective scaling factor = 1
No x scaling provided
No c scaling provided
No d scaling provided
Initial values of x sufficiently inside the bounds.
Initial values of s sufficiently inside the bounds.
MUMPS used permuting_scaling 5 and pivot_order 5.
           scaling will be 77.
Number of doubles for MUMPS to hold factorization (INFO(9)) = 1137
Number of integers for MUMPS to hold factorization (INFO(10)) = 1346
Factorization successful.
Least square estimates max(y_c) = 3.985024e-03, max(y_d) = 0.000000e+00
Total number of variables............................:       70
                     variables with only lower bounds:        0
                variables with lower and upper bounds:       22
                     variables with only upper bounds:        0
Total number of equality constraints.................:       48
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

... (Iteration details of the first run won't be listed here since I think they are not related to the error in the second run and they are just too long)

Number of objective function evaluations             = 10
Number of objective gradient evaluations             = 10
Number of equality constraint evaluations            = 10
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 10
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 9
Total CPU secs in IPOPT (w/o function evaluations)   =      0.012
Total CPU secs in NLP function evaluations           =      0.004

EXIT: Optimal Solution Found.

Cost: 2.05862e-06
timecost in first run: 0.0250772

=============== Second Run ===============

List of user-set options:

                                    Name   Value                used
                            max_cpu_time = 0.5                   yes
                      nlp_scaling_method = none                  yes
                             print_level = 6                     yes
                      print_user_options = yes                   yes
                   warm_start_bound_frac = 1e-16                 yes
                   warm_start_bound_push = 1e-16                 yes
                   warm_start_init_point = yes                   yes
              warm_start_mult_bound_push = 1e-16                 yes
             warm_start_slack_bound_frac = 1e-16                 yes
             warm_start_slack_bound_push = 1e-16                 yes

List of options:

                                    Name   Value                # times used
                            max_cpu_time = 0.5                       1
                      nlp_scaling_method = none                      1
                             print_level = 6                         2
                      print_user_options = yes                       1
                   warm_start_bound_frac = 1e-16                     1
                   warm_start_bound_push = 1e-16                     1
                   warm_start_init_point = yes                       1
              warm_start_mult_bound_push = 1e-16                     1
             warm_start_slack_bound_frac = 1e-16                     1
             warm_start_slack_bound_push = 1e-16                     1
This is Ipopt version 3.12.4, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian...:      191
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:       89

objective scaling factor = 1
No x scaling provided
No c scaling provided
No d scaling provided
cppad-20180000.0 error from unknown source
Error detected by false result for
    init_z == false
at line 596 in the file 
    /usr/include/cppad/ipopt/solve_callback.hpp
motion_control_node: /usr/include/cppad/utility/error_handler.hpp:206: static void CppAD::ErrorHandler::Default(bool, int, const char*, const char*, const char*): Assertion `false' failed.

[bradbell]

CppAD::ipopt::solve does not have a warm start option. I suggest you consider using
https://bradbell.github.io/cppad_mixed/doc/cppad_mixed.htm
In the special case where there are no random effects, you get a normal optimization problem.

It has a warm start option
https://bradbell.github.io/cppad_mixed/doc/warm_start.cpp.htm

[Magic-wei]

Thank you for your reply! Will take a look.