# Package glpk

From ApCoCoAWiki

Revision as of 11:02, 1 November 2020 by Andraschko (talk | contribs) (Created page with "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 o...")

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*: The GLPK-Program glpsol must be in the ApCoCoA package directory /binaries/glpk/examples and you must have the permissions to read and write in this directory.

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

## Usage

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 lists with`l[i]`

if (resp.`u[i]`

if ) and`l[i] = ""`

if (resp.`u[i] = ""`

if ). Furthermore, we 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

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

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

.