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Model.setPWLObj()
setPWLObj ( var, x, y )
Set a piecewise-linear objective function for a variable.
The arguments to this method specify a list of points that define a
piecewise-linear objective function for a single variable.
Specifically, the 
and 
arguments give coordinates for the
vertices of the function.
For example, suppose we want to define the function 
shown below:
, 
and
, so is [1, 3, 5] and is [1, 2, 4]. With these
arguments we define 
, 
and 
. Other
objective values are linearly interpolated between neighboring points.
The first pair and last pair of points each define a ray, so values
outside the specified values are extrapolated from these points.
Thus, in our example, 
and 
.
More formally, a set of 
points
![\begin{displaymath}
\mathtt{x} = [x_1, \ldots, x_n], \quad \mathtt{y} = [y_1, \ldots, y_n]
\end{displaymath}](https://www.gurobi.com/wp-content/plugins/hd_documentations/documentation/11.0/refman/img33.png?x57819){kind=small}
define the following piecewise-linear function:
![\begin{displaymath}
f(v) =
\left\{
\begin{array}{ll}
y_1 + \frac{y_2-y_1}{x_2-x_...
...- x_n), & \mathrm{if}\; v \ge x_n. \ [7pt]
\end{array}\right.
\end{displaymath}](https://www.gurobi.com/wp-content/plugins/hd_documentations/documentation/11.0/refman/img20.png?x57819)
The entries must appear in non-decreasing order. Two points can
have the same coordinate -- this can be useful for specifying a
discrete jump in the objective function.
Note that a piecewise-linear objective can change the type of a model. Specifically, including a non-convex piecewise linear objective function in a continuous model will transform that model into a MIP. This can significantly increase the cost of solving the model.
Setting a piecewise-linear objective for a variable will set the
Obj attribute on that variable to 0.
Similarly, setting the Obj attribute will delete the
piecewise-linear objective on that variable.
Each variable can have its own piecewise-linear objective function. They must be specified individually, even if multiple variables share the same function.
Arguments:
var: A Var object that gives the variable whose objective function is being set.
x: The values for the points that define the piecewise-linear function. Must be in non-decreasing order.
y: The values for the points that define the piecewise-linear function.
Example usage:
model.setPWLObj(var, [1, 3, 5], [1, 2, 4])
