IPOPT Solver Options Not Promoting Int to Float

[cohnt]

What happened?

If you set the max wall clock time in IPOPT to an integer value, it throws an error, but it works correctly if it's a double. Maybe connected to #18024, but it seems like the error is specifically in the IPOPT interface.

from pydrake.all import MathematicalProgram, IpoptSolver, SolverOptions

prog = MathematicalProgram()
x = prog.NewContinuousVariables(1)

options = SolverOptions()
# options.SetOption(IpoptSolver().solver_id(), "max_wall_time", 10) # Fails
options.SetOption(IpoptSolver().solver_id(), "max_wall_time", 10.0) # Works

result = IpoptSolver().Solve(prog, solver_options=options)

Bug output:

Tried to set Option: max_wall_time. It is a valid option, but it is of type  Number, not of type Integer. Please check the documentation for options.

### max_wall_time (Real Number)  ###
Category: Termination
Description: Maximum number of walltime clock seconds.
0 < (1e+20) <= +inf
Traceback (most recent call last):
  File "/home/tommy/temp.py", line 10, in <module>
    result = IpoptSolver().Solve(prog, solver_options=options)
RuntimeError: Error setting IPOPT integer option max_wall_time=10

Version

No response

What operating system are you using?

No response

What installation option are you using?

No response

Relevant log output

[jwnimmer-tri]

To solve this, I believe we would need to ask the IpoptApplication for its RegOptions() and then check the registered type of the option name, to know if we need to promote int to float. This would be in solvers/ipopt_solver.cc inside our SetAppOptions.

[sherm1]

Assigned to @hongkai-dai for disposition.