Elias at 14:53, 22 July 2011

2011-07-22T14:53:30Z

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			[[Category:Utility Functions]]
	==Purpose==		==Purpose==

Elias: Created page with "==Purpose== Adds piecewise linear function to a TOMLAB MIP problem. ==Calling Syntax== There are two ways to call addPwLinFun: Syntax 1:

 function Prob = addPwLinFun(..."

2011-07-22T09:42:18Z

Created page with "==Purpose== Adds piecewise linear function to a TOMLAB MIP problem. ==Calling Syntax== There are two ways to call addPwLinFun: Syntax 1: <pre> function Prob = addPwLinFun(..."

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==Purpose==

Adds piecewise linear function to a TOMLAB MIP problem.

==Calling Syntax==

There are two ways to call addPwLinFun:

Syntax 1:
<pre>
function Prob = addPwLinFun(Prob, 1, type, var, funVar, point, slope, a, fa)
</pre>

Syntax 2:
<pre>
function Prob = addPwLinFun(Prob, 2, type, var, funVar, firstSlope, point, value, lastSlope)
</pre>

==Inputs==

{| class="wikitable"
!Input||Description
|-
|''Prob''||The problem to add the function to.
|-valign="top"
|''input''||Flag indicating syntax used.
|-valign="top"
|''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'.
|-valign="top"
|''var''||The number of the variable on which the piecewise linear function depends. Must exist in the problem already.
|-valign="top"
|''funVar''||The number of the variable which will be equal to the piecewise linear function. Must exist in the problem already.
|-valign="top"
|''firstSlope''||Syntax 2 only. The slope of the piecewise linear function left of the first point, point(1).
|-valign="top"
|''point''||An array of break points. Must be sorted. If two values occur twice, there is a step at that point. Length r.
|-valign="top"
|''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.
|-valign="top"
|''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.
|-valign="top"
|''lastSlope''||Syntax 2 only. The slope of the piecewise linear function right of the last point, point(r).
|-valign="top"
|''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==
{| class="wikitable"
!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'.

AddPwLinFun - Revision history

Elias at 14:53, 22 July 2011

Elias: Created page with "==Purpose== Adds piecewise linear function to a TOMLAB MIP problem. ==Calling Syntax== There are two ways to call addPwLinFun: Syntax 1:
function Prob = addPwLinFun(..."