Created
November 2, 2025 07:08
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Solves this stackoverflow question: https://stackoverflow.com/questions/68266571/how-to-speed-up-the-ipopt-solver/
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| import numpy as np | |
| import sympy as sm | |
| import matplotlib.pyplot as plt | |
| from opty import Problem, create_objective_function | |
| t = sm.symbols('t', real=True) | |
| x1, x2, v = sm.Function('x1')(t), sm.Function('x2')(t), sm.Function('v')(t) | |
| eqs = sm.Matrix([x1.diff() - x1 + x1*x2 + 0.4*x1*v, | |
| x2.diff() + x2 - x1*x2 + 0.2*x2*v]) | |
| bounds = {v: (0.0, 1.0)} | |
| instance = (x1.func(0.0) - 0.5, x2.func(0.0) - 0.7) | |
| duration = 12.0 | |
| num_nodes = 48 | |
| h = duration/(num_nodes - 1) | |
| obj_func = sm.Integral((x1 - 1)**2 + (x2 - 1)**2, t) | |
| obj, obj_grad = create_objective_function( | |
| obj_func, | |
| (x1, x2), | |
| (v,), | |
| tuple(), | |
| num_nodes, | |
| h, | |
| time_symbol=t, | |
| ) | |
| p = Problem( | |
| obj, | |
| obj_grad, | |
| eqs, | |
| (x1, x2), | |
| num_nodes, | |
| h, | |
| instance_constraints=instance, | |
| bounds=bounds, | |
| time_symbol=t, | |
| ) | |
| sol, info = p.solve(np.ones(p.num_free)) | |
| p.plot_trajectories(sol) | |
| plt.show() |
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