# Python equivalent of the ComplexUserFunction.c example in
# examples/nonlinear/c directory.
#
# Define objective and constraint as user functions that return
# derivatives:
#
# Minimize myobj (y,z,v,w)
# s.t.
# ball (x,t) <= 730
# 1 <= x <= 2
# 2 <= y <= 3
# 3 <= z <= 4
# 4 <= v <= 5
# 5 <= w <= 6
#
# where
#
# myobj (y,z,v,w) = y**2 + z - v + w**2
# ball (x,t) = x**2 + t**2
#
# (C) 1983-2025 Fair Isaac Corporation
import xpress as xp
def myobj(y, z, v, w):
"""Return value of the objective function with the derivative w.r.t. all variables passed."""
return (y**2 + z - v + w**2, # value of the function
2*y, # derivative w.r.t. y
1, # derivative w.r.t. z
-1, # derivative w.r.t. v
2*w) # derivative w.r.t. w
def ball(x, t):
"""Return value of the left-hand side of the constraint with its derivatives."""
return (x**2 + t**2,
2*x,
2*t)
def myobj_noderiv(y, z, v, w):
"""Return objective without derivatives."""
return y**2 + z - v + w**2 # Value of the function.
def ball_noderiv(x, t):
"""Return left-hand side of constraint without derivatives."""
return x**2 + t**2
def solve_problem(incder):
"""Construct and solve the problem with or without derivatives.
:param incder: True for including derivatives, False otherwise
:return:
"""
p = xp.problem()
x = p.addVariable(lb=1, ub=2)
y = p.addVariable(lb=2, ub=3)
z = p.addVariable(lb=3, ub=4)
v = p.addVariable(lb=4, ub=5)
w = p.addVariable(lb=5, ub=6)
t = p.addVariable(lb=-xp.infinity) # Free variable.
p.setObjective(t)
if incder:
p.addConstraint(t == xp.user(myobj, y, z, v, w, derivatives=True))
p.addConstraint(xp.user(ball, x, t, derivatives=True) <= 730)
print('Solving problem using derivatives:')
else:
p.addConstraint(t == xp.user(myobj_noderiv, y, z, v, w))
p.addConstraint(xp.user(ball_noderiv, x, t) <= 730)
print('Solving problem without using derivatives:')
# With user functions the problem cannot be solved to
# global optimality, so the control below is not necessary
# but shown here for completeness. Setting nlpsolver to one
# ensures the problem is solved by a local solver rather than the
# global solver.
p.controls.nlpsolver = xp.constants.NLPSOLVER_LOCAL
p.optimize()
print('Problem solved. Objective:', p.attributes.objval, '; solution:', p.getSolution())
if __name__ == '__main__':
solve_problem(True)
solve_problem(False)
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