IPOPT

IPOPT (Interior Point OPTimizer) is a gradient-based optimization algorithm that uses an interior point method to solve general nonlinear programming problems. It can utilize second-order derivative information in the form of the Hessian of the objective for unconstrained problems or the Hessian of the Lagrangian for constrained problems. This solver uses the ‘ipopt’ algorithm from the CasADi library.

To use the IPOPT solver in modOpt, first install CasADi with pip install casadi. You can then import the IPOPT solver from modOpt as shown in the following code:

from modopt import IPOPT

Options for the IPOPT solver are available here. Solver options could be set by just passing them within the solver_options dictionary when instantiating the IPOPT optimizer object. For example, we can set the maximum number of iterations max_iter and the convergence tolerance tol for the algorithm as shown below.

optimizer = IPOPT(prob, solver_options={'max_iter': 100, 'tol': 1e-6})

Some of the most commonly applicable options are given below:

IPOPT solver options

Option	Type (default value)	Description
max_iter	int (1000)	Maximum number of iterations.
max_wall_time	float (1e+20)	Maximum number of walltime clock seconds.
max_cpu_time	float (1e+20)	Maximum number of cpu seconds.
tol	float (1e-8)	Convergence tolerance for the algorithm.
print_level	int (5)	Controls the verbosity level for the console output. Valid range is between 0 and 12. The output becomes more detailed as this value increases.
output_file	str ("ipopt_output.txt")	Output filename.
file_print_level	int (5)	Controls the verbosity level for the output file. Valid range is between 0 and 12. The file output becomes more detailed as this value increases.
file_append	str ("no")	Determines whether to append to the output file. Valid values are "yes" or "no".
print_user_options	str ("yes")	Determines whether to print all options set by the user. Valid values are "yes" or "no".
print_advanced_options	str ("no")	Determines whether to print the advanced options also. Valid values are "yes" or "no".
linear_solver	str ("mumps")	Linear solver to use for computing the step direction. Valid values are “ma27”, “ma57”, “ma77”, “ma86”, “ma97”, “pardiso”, “pardisomkl”, “spral”, “wsmp”, “mumps”, or “custom”.
hessian_approximation	str ("limited-memory")	Set "exact" to force IPOPT to use user-defined second derivatives (objective/Lagrangian Hessian for unconstrained/constrained problems). Default is “limited-memory” which uses a limited-memory quasi-Newton Hessian approximation.
print_timing_statistics	str ("no")	Set "yes" to measure and print time spent on selected tasks.
derivative_test	str ("none")	To perform a derivative check at the at the initial guess x0 before the optimization. Possible values are: "none" : turn off derivative test "first-order" : check first derivatives "second-order" : check both first and second derivatives "only-second-order" : check only second derivatives
derivative_test_print_all	str ("no")	Set "yes" to print information for all derivatives tested. Default is "no" which prints information only for derivatives with relative error > derivative_test_tol.
derivative_test_perturbation	float (1e-8)	Relative size of the finite difference perturbation in derivative test.
derivative_test_tol	float (1e-4)	Indicate derivatives as wrong if: relative error > derivative_test_tol.