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#
# MIT No Attribution
#
# Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl, KU Leuven.
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this
# software and associated documentation files (the "Software"), to deal in the Software
# without restriction, including without limitation the rights to use, copy, modify,
# merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
# permit persons to whom the Software is furnished to do so.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
# INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
# PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
# OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
#
from casadi import *
"""
Solve the Rosenbrock problem, formulated as the NLP:
minimize x^2 + 100*z^2
subject to z+(1-x)^2-y == 0
Joel Andersson, 2015
"""
# Declare variables
x = SX.sym("x")
y = SX.sym("y")
z = SX.sym("z")
# Formulate the NLP
f = x**2 + 100*z**2
g = z + (1-x)**2 - y
nlp = {'x':vertcat(x,y,z), 'f':f, 'g':g}
# Create an NLP solver
solver = nlpsol("solver", "ipopt", nlp)
# Solve the Rosenbrock problem
res = solver(x0 = [2.5,3.0,0.75],
ubg = 0,
lbg = 0)
# Print solution
print()
print("%50s " % "Optimal cost:", res["f"])
print("%50s " % "Primal solution:", res["x"])
print("%50s " % "Dual solution (simple bounds):", res["lam_x"])
print("%50s " % "Dual solution (nonlinear bounds):", res["lam_g"])
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