Many solvers allow the users to adjust the parameters. When calling Solve() function, Drake will use the default parameters for the solver (iterations, optimality tolerance, etc). You could modify these parameters in two ways, by either calling MathematicalProgram::SetSolverOption, or pass a SolverOptions argument to the Solve() function.
By calling MathematicalProgram::SetSolverOption(solver_id, option_name, option_value), you can set a parameter for a specific solver (with the matching solver_id). The option_name is specific to that solver (for example, here is a list of IPOPT parameters). Note that MathematicalProgram object will store this solver parameter, and this parameter will be applied in the Solve() call, if that specific solver (with the matching solver_id) is invoked.
In the following code snippet, we show an example of setting the options of IPOPT.
from pydrake.solvers import MathematicalProgram, SolverOptions, Solve
from pydrake.solvers import IpoptSolver
import numpy as np
prog = MathematicalProgram()
x = prog.NewContinuousVariables(2)
prog.AddCost(x[0]**2 + x[1] ** 2)
prog.AddConstraint(x[0] + x[1] == 1)
# Set the maximum iteration for IPOPT to be 1.
# max_iter is a parameter of IPOPT solver, explained in
# https://www.coin-or.org/Ipopt/documentation/node42.html
prog.SetSolverOption(IpoptSolver().solver_id(), "max_iter", 1)
solver = IpoptSolver()
result = solver.Solve(prog, np.array([10, 1]), None)
# With fewer maximum iteration, IPOPT hasn't converged to optimality yet (The true optimal is [0.5, 0.5])
print("Success? ", result.is_success())
print(result.get_solution_result())
print("IPOPT x*= ", result.GetSolution(x))
WARNING:drake:IPOPT terminated after exceeding the maximum iteration limit. Hint: Remember that IPOPT is an interior-point method and performs badly if any variables are unbounded.
Success? False SolutionResult.kIterationLimit IPOPT x*= [-4. 5.]
Also note that setting the parameter of a solver doesn't mean that result = Solve(prog) will invoke that solver. The invoked solver is determined by Drake, to choose whichever solver it thinks most appropriate.
In the following snippet, although we set the solver options for IPOPT, Drake chooses another solver (which can solve this particular problem in the closed form.)
prog.SetSolverOption(IpoptSolver().solver_id(), "max_iter", 1)
result = Solve(prog)
print(result.get_solver_id().name())
EqConstrainedQP
Another way of setting the solver options is to pass in a SolverOptions object as an argument to Solve function. MathematicalProgram will not store this SolverOptions object.
In the following example, in the first Solve call, it uses the SolverOptions object to set the parameter for IPOPT; in the second Solve call, it uses the default IPOPT parameters, hence we get different results from two Solve calls.
prog = MathematicalProgram()
x = prog.NewContinuousVariables(2)
prog.AddCost(x[0]**2 + x[1] ** 2)
prog.AddConstraint(x[0] + x[1] == 1)
solver_options = SolverOptions()
solver_options.SetOption(IpoptSolver().solver_id(), "max_iter", 1)
solver = IpoptSolver()
# Call Solve with solver_options, IPOPT will use `max_iter` = 1
result = solver.Solve(prog, np.array([10, 1]), solver_options)
print("Success? ", result.is_success())
print(result.get_solution_result())
# Call Solve without solver_options, IPOPT will use the default options.
result = solver.Solve(prog, np.array([10, 1]), None)
print("Success? ", result.is_success())
print(result.get_solution_result())
WARNING:drake:IPOPT terminated after exceeding the maximum iteration limit. Hint: Remember that IPOPT is an interior-point method and performs badly if any variables are unbounded.
Success? False SolutionResult.kIterationLimit Success? True SolutionResult.kSolutionFound