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63.1 Introduction to simplex | ||
63.2 Definitions for simplex |
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simplex
is a package for linear optimization using the simplex algorithm.
Example:
(%i1) load("simplex")$ (%i2) minimize_sx(x+y, [3*x+2*y>2, x+4*y>3]); 9 7 1 (%o2) [--, [y = --, x = -]] 10 10 5 |
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Default value: 10^-8
Epsilon used for numerical computations in linear_program
.
See also: linear_program
.
linear_program
is an implementation of the simplex algorithm.
linear_program(A, b, c)
computes a vector x for which c.x
is minimum
possible among vectors for which A.x = b
and x >= 0
. Argument
A is a matrix and arguments b and c are lists.
linear_program
returns a list which contains the minimizing vector x and the
minimum value c.x
. If the problem is not bounded, it returns "Problem not bounded!" and
if the problem is not feasible, it returns "Problem not feasible!".
To use this function first load the simplex
package with load(simplex);
.
Example:
(%i2) A: matrix([1,1,-1,0], [2,-3,0,-1], [4,-5,0,0])$ (%i3) b: [1,1,6]$ (%i4) c: [1,-2,0,0]$ (%i5) linear_program(A, b, c); 13 19 3 (%o5) [[--, 4, --, 0], - -] 2 2 2 |
See also: minimize_sx
, scale_sx
, and epsilon_sx
.
Maximizes linear objective function obj subject to some linear constraints
cond. See minimize_sx
for detailed description of arguments and return
value.
See also: minimize_sx
.
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_sx
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_sx
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_sx
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_sx
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_sx(x+y, [3*x+y=0, x+2*y>2]); 4 6 2 (%o1) [-, [y = -, x = - -]] 5 5 5 (%i2) minimize_sx(x+y, [3*x+y>0, x+2*y>2]), nonegative_sx=true; (%o2) [1, [y = 1, x = 0]] (%i3) minimize_sx(x+y, [3*x+y=0, x+2*y>2]), nonegative_sx=true; (%o3) Problem not feasible! (%i4) minimize_sx(x+y, [3*x+y>0]); (%o4) Problem not bounded! |
See also: maximize_sx
, nonegative_sx
, epsilon_sx
.
Default value: false
If nonegative_sx
is true all decision variables to minimize_sx
and maximize_sx
are assumed to be positive.
See also: minimize_sx
.
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