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Create a problem with piecewise linear functions Description Create a simple problem using the modeling construct xpress.pwl (in piecewise_linear.py)
and the API function problem.addpwlcons (in piecewise_linear2.py) for creating piecewise linear functions. Further explanation of this example: 'Xpress Python Reference Manual'
Source Files By clicking on a file name, a preview is opened at the bottom of this page.
piecewise_linear.py
# Example that uses the xpress.pwl() method to approximate nonlinear
# univariate functions.
#
# (C) 1983-2025 Fair Isaac Corporation
import xpress as xp
import math
import numpy as np
p = xp.problem() # Create a problem and add variable x.
x = p.addVariable(ub=4)
# Piecewise linear, continuous concave function.
pw1 = xp.pwl({(0, 1): 10*x,
(1, 2): 10 + 3*(x-1),
(2, 3): 13 + 2*(x-2),
(3, 4): 15 + (x-3)})
# Approximate sin(freq * x) for x in [0, 2*pi].
N = 100 # Number of points of the approximation.
freq = 27.5 # Frequency.
step = 2 * math.pi / (N - 1) # Width of each x segment.
breakpoints = np.array([i * step for i in range(N)])
values = np.sin(freq * breakpoints) # Value of the function.
slopes = freq * np.cos(freq * breakpoints) # Derivative.
# Piecewise linear, discontinuous function over N points: over the
# i-th interval, the function is equal to v[i] + s[i] * (y - b[i])
# where v, s, b are value, slope, and breakpoint.
pw2 = xp.pwl({(breakpoints[i], breakpoints[i+1]):
values[i] + slopes[i] * (x - breakpoints[i]) for i in range(N - 1)})
p.setObjective (pw1 - pw2)
p.optimize()
print("solution: x = ", p.getSolution(x))
print("values of piecewise linear functions:", xp.evaluate([pw1, pw2], problem=p))
print("objective function:", p.attributes.objval)
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| © Copyright 2025 Fair Isaac Corporation. |
