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Create a problem with piecewise linear functions Description Create a simple problem using the modelling construct xpress.pwl for creating piecewise linear functions. Further explanation of this example:
'Xpress Python Reference Manual'
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piecewise_linear.py # Example that uses the xpress.pwl method to approximate nonlinear # univariate functions. # # (C) Fair Isaac Corp., 1983-2021 import xpress as xp import math import numpy as np x = xp.var(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 = xp.problem(x) # create a problem and add variable x p.setObjective (pw1 - pw2) p.solve() print("solution: x = ", p.getSolution(x)) print("values of piecewise linear functions:", xp.evaluate([pw1, pw2], problem=p)) print("objective function:", p.getObjVal()) | |||||||||||

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