Package glpk

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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].