Adds one or more piecewise linear constraints to the problem. Each piecewise linear constraint y = f(x) consists of an (input) column x, a resultant (output column) y and a piecewise linear function f. The piecewise linear function f is described by a number of breakpoints, which are given as combinations of x- and y-values. Discontinuous piecewise linear functions are supported, in this case both the left and right limit at a given point need to be entered as breakpoints. To differentiate between left and right limit, the breakpoints need to be given as a list with non-decreasing x-values.

This adds a new piecewise linear constraint y = f(x), where

f(x) = -x	if x < 0
f(x) = 1	if 0 <= x <= 2
f(x) = 2x-3	if x > 2

col = [x]
resultant = [y]
start = [0]
xval = [-1, 0, 0, 2, 3]
yval = [1, 0.5, 1, 1, 3]

prob.addpwlcons(col, resultant, start, xval, yval)
prob.setObjective(y)   # the piecewise linear function is to be minimized
prob.mipoptimize()

Piecewise linear constraints must be set up before solving the problem. They are converted to additional linear constraints, continuous variables and SOS2 constraints, with the exact formulation and number of added entities depending on the convexity of the piecewise linear function and some presolving steps that are applied.

problem.getpwlcons, problem.delpwlcons, xpress.pwl.