Is it possible to identify unbounded variables?

Question

While attempting to solve my mathematical program, I get the following error

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.

(I'm using IPOPT because I think it is the only free solver available)

Is there any way to identify which variables are unbounded in order to help debug the issue?

Answer 1

Drake's MathematicalProgram returns all the bounds in bounding_box_constraints() function, you could query each of the bounding box constraint and get the bounds on the variables. Here is the python code

# We will store the lower and upper bound of each variable in x_lo and x_up.
x_lo = np.full((prog.num_vars(),), -np.inf)
x_up = np.full((prog.num_vars(),), np.inf)
for bb_con in prog.bounding_box_constraints():
    # loop over each bounding box constraint
    for i in range(bb_con.variables().shape[0]):
        # loop over each variable associated with the constraint. First find the index of the variable
        var_index = int(prog.decision_variable_index()[bb_con.variables()[i].get_id()])
        # Update the lower bound for the variable.
        x_lo[var_index] = np.max((x_lo[var_index], bb_con.evaluator().lower_bound()[i]))
        # Update the upper bound for the variable.
        x_up[var_index] = np.min((x_up[var_index], bb_con.evaluator().upper_bound()[i]))
# now x_lo and x_up stores the bounds for each variable
for i in range(prog.num_vars()):
    if np.isinf(x_lo[i]) and np.isinf(x_up[i]):
        # print out the variable with no lower and upper bound.
        print(prog.decision_variables()[i])