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Use the API to create a model with piecewise linear functions

Description
Create a simple problem using the API function problem.addpwlcons to create piecewise linear functions. The resulting model is equivalent to piecewise_linear.py.

Further explanation of this example: 'Xpress Python Reference Manual'

Source Files
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piecewise_linear2.py

# Example that uses the xpress.pwl method to approximate nonlinear
# univariate functions. This is equivalent to piecewise_linear.py,
#
# (C) Fair Isaac Corp., 1983-2021

import xpress as xp
import math
import numpy as np

x = xp.var(ub=4)

# When using the API functions, we have to define new variables. Note
# that for defining a function that is unrestricted in sign we have to
# define a free variable
y1 = xp.var()
y2 = xp.var(lb=-xp.infinity)

# 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

# Create new problem with three variables
p = xp.problem(x, y1, y2)

values2 = values + slopes * step

[y1, y2],  # variables defined as piecewise linear
[0, 4],    # starting points, within the following
# two lists, of the points of each function.

# x values:
# for the first pwl function, the breakpoints 0,1,2,3
[0,  1,  2,  3] +
# for the second one, we alternate between the beginning
# and the end of each segment. Note that we use both
# beginning and end of each interval.
list(np.hstack(np.array([breakpoints[:-1],breakpoints[1:]]).transpose())),

# y values:
# for the first pwl function, the corresponding values of
# the function.
[0, 10, 13, 15] +
# similar to the above, for the second one we add the y
# values for both beginning and end of each segment,
# because of the discontinuity.
list(np.hstack(np.array([values[:-1],values2[:-1]]).transpose())))

# The objective is the difference of the two variables defined as
# piecewise linear functions.
p.setObjective (y1 - y2)

p.solve()

print("solution: x = ", p.getSolution(x))
print("values of piecewise linear functions:", p.getSolution(y1,y2))
print("objective function:", p.getObjVal())