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Approximating nonlinear univariate functions via piecewise linear constraints Description Approximating nonlinear univariate functions using
piecewise linear constraints.
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piecewise_linear.mos (!****************************************************** Mosel Example Problems ====================== file piecewise_linear.mos ````````````````````````` Approximating nonlinear univariate functions using piecewise linear constraints. -- Mosel version of the Python example piecewise_linear.py -- (c) 2020 Fair Isaac Corporation author: Y.Colombani, Jun. 2020 *******************************************************!) model piecewise_linear uses 'mmxnlp' parameters N = 100 ! Number of points of the approximation FREQ = 27.5 ! Frequency of sine curve end-parameters public declarations STEP = 2 * M_PI / (N - 1) ! Width of each x segment x: mpvar end-declarations ! Piecewise linear, continuous concave function formulated via piecewise ! linear segments pw1:= pwlin([pws(0, 10*x), pws(1, 10 + 3*(x-1)), pws(2, 13 + 2*(x-2)), pws(3, 15 + (x-3))]) !**** Approximate sin(FREQ * x) for x in [0, 2*pi] ! Piecewise linear, discontinuous function over N points: over the ! i-th interval, the function is equal to v[i] + s[i] * (x - b[i]) ! where v, s, b are value, slope, and breakpoint. pw2:= pwlin(union(i in 0..N-1,s=i*STEP)[pws(s,sin(s*FREQ)+FREQ*cos(s*FREQ)*(x-s))]) minimise(pw1 - pw2) writeln("solution: x = ", x.sol) writeln("values of piecewise linear functions:", [pw1.sol, pw2.sol]) writeln("objective function:", getobjval) end-model | |||||||||||

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