GRBModel.SetPWLObj()

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, theandarguments give coordinates for the vertices of the function.

For example, suppose we want to define the functionshown below:

The vertices of the function occur at the points

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 ofpoints

$\begin{displaymath} \mathtt{x} = \{x_1, \ldots, x_n\}, \quad \mathtt{y} = \{y_1, \ldots, y_n\} \end{displaymath}$

define the following piecewise-linear function:

$\begin{displaymath} f(v) = \left\{ \begin{array}{ll} y_1 + \frac{y_2-y_1}{x_2-x_... ...- x_n), & \mathrm{if}\; v \ge x_n. \ [7pt] \end{array}\right. \end{displaymath}$

Theentries must appear in non-decreasing order. Two points can have the samecoordinate -- 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 theObj attributeon that variable to 0. Similarly, setting theObjattribute 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.

void	SetPWLObj(	GRBvar	var,
		double[]	x,
		double[]	y )

Arguments:

var: The variable whose objective function is being set.

x: Thevalues for the points that define the piecewise-linear function. Must be in non-decreasing order.

y: Thevalues for the points that define the piecewise-linear function.