Initializing help system before first use

problem.addpwlcons

Purpose
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.
Synopsis
problem.addpwlcons(colind, resultant, start, xval, yval)
Arguments
colind 
Integer array (or list) containing the input variables x of the piecewise linear functions.
resultant 
Integer array containing the output variables y of the piecewise linear functions.
start 
Integer array containing the start index of each piecewise linear constraint in the xval and yval arrays.
xval 
Array containing the x-values of the breakpoints.
yval 
Array containing the y-values of the breakpoints.
Example
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

This function can be defined using the breakpoints (x = -1, y = 1), (0,0), (0,1), (2,1), (3,3) (note that the first breakpoint could also be replaced, e.g., by (x = -2, y = 2), similarly for the last): 
colind = [x]
resultant = [y]
start = [0]
xval = [-1, 0, 0, 2, 3]
yval = [ 1, 0, 1, 1, 3]

prob.addpwlcons(colind, resultant, start, xval, yval)
prob.setObjective(y)   # the piecewise linear function is to be minimized
prob.mipoptimize()
Further information
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.
Related topics
problem.getpwlcons, problem.delpwlcons, xpress.pwl.

Parent Topic Xpress problem methods

© 2001-2024 Fair Isaac Corporation. All rights reserved. This documentation is the property of Fair Isaac Corporation (“FICO”). Receipt or possession of this documentation does not convey rights to disclose, reproduce, make derivative works, use, or allow others to use it except solely for internal evaluation purposes to determine whether to purchase a license to the software described in this documentation, or as otherwise set forth in a written software license agreement between you and FICO (or a FICO affiliate). Use of this documentation and the software described in it must conform strictly to the foregoing permitted uses, and no other use is permitted.