ApCoCoA-1:GLPK.LPMin

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GLPK.LPMin

Solving linear programmes by minimizing the objective function.

Syntax

GLPK.LPMin(Objective_f:POLY, Inequations:LIST, Bounds:LIST, Method:STRING) :LIST

Description

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  • @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 programm 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 archieved

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]


Latte.Minimize