Use the API to create a model with piecewise linear functions
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'
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# Example that uses the xpress.pwl method to approximate nonlinear # univariate functions. This is equivalent to piecewise_linear.py, # where we use xpress.pwl instead of problem.addpwlcons for # readability. # # (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 p.addpwlcons([x, x], # independent variables [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())
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