AddPwLinFun

Purpose

Adds piecewise linear function to a TOMLAB MIP problem.

Calling Syntax

There are two ways to call addPwLinFun:

Syntax 1:

function Prob = addPwLinFun(Prob, 1, type, var, funVar, point, slope, a, fa)

Syntax 2:

function Prob = addPwLinFun(Prob, 2, type, var, funVar, firstSlope, point, value, lastSlope)

Inputs

Input	Description
Prob	The problem to add the function to.
input	Flag indicating syntax used.
type	A string telling whether to construct a general MIP problem or to construct an MIP problem only solvable by CPLEX. Possible values: 'mip', 'cplex'.
var	The number of the variable on which the piecewise linear function depends. Must exist in the problem already.
funVar	The number of the variable which will be equal to the piecewise linear function. Must exist in the problem already.
firstSlope	Syntax 2 only. The slope of the piecewise linear function left of the first point, point(1).
point	An array of break points. Must be sorted. If two values occur twice, there is a step at that point. Length r.
slope	Syntax 1 only. An array of the slopes of the segments. slope(i) is the slope between point(i-1) and point(i). slope(1) is the slope of the function left of point(1). slope(r+1) is the slope of the function right of point(r). If points(i-1) == points(i), slope(i) is the height of the step.
value	Syntax 2 only. The values of the piecewise linear function at the points given in point. f(point(i)) = value(i). If point(i-1) == point(i), value(i-1) is the right limit of the value at the point, and value(i) is the left limit of the value at the point.
lastSlope	Syntax 2 only. The slope of the piecewise linear function right of the last point, point(r).
a, fa	Syntax 1 only. The value of the piecewise linear function at point a is equal to fa. f(a) = fa, that is.

Outputs

Output	Description
Prob	The new problem structure with the piecewise linear function added. New variables and linear constraints added. (MIP problem)

Description

This function will make one already existing variable of the problem to be constrained equal to a piecewise linear function of another already existing variable in the problem. The independent variable must be bounded in both directions.

The variable constrained to be equal to a piecewise linear function can be used like any other variable; in constraints or the objective function.

Depending on how many segments the function consists of, a number of new variables and constraints are added to the problem.

Increasing the upper bound (x_U) or decreasing the lower bound (x_L) of the independent variable after calling this function will ruin the piecewise linear function.

If the problem is to be solved by CPLEX, set type = 'cplex' to enhance performance. Otherwise, let type = 'mip'. NOTICE! You can not solve a problem with another solver than CPLEX if type = 'cplex'.