# Package glpk

This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see Category:ApCoCoA-1:Package glpk. |

This page describes the glpk package. For a complete list of functions, see Category:Package glpk.

The basic idea behind this package is to make the linear optimization program GLPK usable in/with ApCoCoA. The package GLPK contains various functions that let you make use of the GLPK library, rather the stand-alone LP/MIP Solver glpsol.

*Important*: For usage under linux, the GLPK-Program glpsol must be in the ApCoCoA package directory under `packages/binaries/glpk/examples/glpsol`

and you must have the permissions to read and write in this directory. For Windows, the glsol.exe has to be in the folder `packages\binaries\glpk\w64\glpsol.exe`

. If you installed ApCoCoA-2 together with the GUI, this should already be the case.

The source code of GLPK can be downloaded at [1].

## Optimizing Linear Systems Of Equations

*See also: GLPK.LPSolve*

Let and . Let be linear polynomials and let . Let be the system of polynomial (in)equations

Then the function `GLPK.LPSolve`

can be used to find solution to such that in the following way.

- Let
`EQ`

be the list , let`LE`

be the list , and let`GE`

be the list . - Let
`l`

and`u`

be the lists containing the upper and lower bounds for the with`l[i]`

and`u[i]`

, if both are rational numbers. Instead of and , write`l[i] = ""`

or`u[i] = ""`

. Set`B := [ [l[1],u[1]], [l[2],u[2]], ..., [l[n],u[n]] ]`

. - Choose a string
`Method`

from`[ "InterP", "Simplex" ]`

depending on the method you want GLPK to use for solving the problem (`"InterP"`

stands for the inter-point-method and`"Simplex"`

for the simplex method) - Choose a string
`MinMax`

from`[ "Min", "Max" ]`

depending on whether you want to fulfill or .

Then call

GLPK.LPSolve(c,EQ,LE,GE,B,Method,MinMax)

to get the desired solution as a list `b = [b1,...,bn]`

or the empty list `[]`

if the given system of (in)equalities is unsatisfiable.

## Solving Mixed Integer Problems

*See also: GLPK.MIPSolve*

Let be disjoint sets. If additionally, a solution with for and for is searched, then one can use the function `GLPK.MIPSolve`

. Together with `c`

, `EQ`

, `LE`

, `GE`

, `B`

and `MinMax`

from above, the code

GLPK.MIPSolve(c,EQ,LE,GE,B,I,J,MinMax)

produces the desired solution or `[]`

if the given system has no such solution.