Difference between revisions of "ApCoCoA-1:GLPK.LPMin"
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Revision as of 16:13, 2 October 2020
GLPK.LPMin
Solving linear programmes by minimizing the objective function.
Syntax
GLPK.LPMin(Objective_f:POLY, Inequations:LIST, Bounds:LIST, Method:STRING) :LIST
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
@param Objective_f: A linear polynomial which is equivalent to the linear objective function.
@param Inequations: List of linear polynomials, which are equivalent to the conditions of the linear program of the form A <= 0.
@param Bounds: List of lists with two elements. Each List contains the lower and upper bounds for each variable. You can choose between INT or RAT for the type of each bound, if you type in a (empty) string, then it means minus infinity (first place) or plus infinity (second place).
@param Method: You can choose between the interior-point-method ("InterP") or the simplex-algorithm ("Simplex"). Usually you should use the simplex-algorithm.
@return List of linear polynomials, the zeros of the polynomials are the points where the optimal value of the objective function is achieved
Example
Use S::=QQ[x,y]; OF := 1/2x + y; IE := [3/4x + y - 6, -x - y + 1]; Bounds:=[[0,6], [1/3,4]]; -- Then we compute the solution with GLPK.LPMin(OF, IE, Bounds, <quotes>Simplex</quotes>); -- And we achieve: ------------------------------------- Solution Status: OPTIMAL Value of objective function: 5333333333/1000000000 [x[1] - 266667/100000, x[2] - 4]
