Cost Vector

The functions maximize and minimize solve the integer linear programs

$$\max\{c^\intercal x: x\in P\cap{\mathbb{Z}}^d\}$$

and

$$\min\{c^\intercal x: x\in P\cap{\mathbb{Z}}^d\}.$$

Besides a description of the polyhedron $P$ , these functions need a linear objective function given by a certain cost vector $c$ . If the polyhedron is given in the file ``fileName''

4  4
1 -1  0  0
1  0 -1  0
1  0  0 -1
1 -1 -1 -1
linearity 1 4
nonnegative 3 1 2 3

the cost vector must be given in the file ``fileName.cost'', as for example in the following three-dimensional problem:

1 3
2 4 7

The first two entries state the size of a $1\times n$ matrix (encoding the cost vector), followed by the $1\times n$ matrix itself. Assuming that we call maximize, this whole data encodes the integer program

$$\max\{2x_1+4x_2+7x_3: x_1+x_2+x_3=1, x_1,x_2,x_3\in\{0,1\}\}.$$