Package glpk

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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


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


produces the desired solution or [] if the given system has no such solution.