minimalPoly SciMax Toolbox minor

SciMax Toolbox >> minimize_lp

minimize_lp

Maxima Function

Calling Sequence

minimize_lp (obj, cond, [pos])

Description

Minimizes a linear objective function obj subject to some linear constraints cond. cond a list of linear equations or inequalities. In strict inequalities > is replaced by >= and < by <=. The optional argument pos is a list of decision variables which are assumed to be positive.

If the minimum exists, minimize_lp returns a list which contains the minimum value of the objective function and a list of decision variable values for which the minimum is attained. If the problem is not bounded, minimize_lp returns "Problem not bounded!" and if the problem is not feasible, it returns "Ploblem not feasible!".

The decision variables are not assumed to be nonegative by default. If all decision variables are nonegative, set nonegative_lp to true. If only some of decision variables are positive, list them in the optional argument pos (note that this is more efficient than adding constraints).

minimize_lp uses the simplex algorithm which is implemented in maxima linear_program function.

To use this function first load the simplex package with load(simplex);.

Examples:

(%i1) minimize_lp(x+y, [3*x+y=0, x+2*y>2]);
                      4       6        2
(%o1)                [-, [y = -, x = - -]]
                      5       5        5
(%i2) minimize_lp(x+y, [3*x+y>0, x+2*y>2]), nonegative_lp=true;
(%o2)                [1, [y = 1, x = 0]]
(%i3) minimize_lp(x+y, [3*x+y=0, x+2*y>2]), nonegative_lp=true;
(%o3)                Problem not feasible!
(%i4) minimize_lp(x+y, [3*x+y>0]);
(%o4)                Problem not bounded!

See also: , , .

minimalPoly SciMax Toolbox minor