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| 70.1 Introduction to simplex | ||
| 70.2 Functions and Variables for simplex |
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simplex is a package for linear optimization using the simplex algorithm.
Example:
(%i1) load("simplex")$
(%i2) minimize_lp(x+y, [3*x+2*y>2, x+4*y>3]);
9 7 1
(%o2) [--, [y = --, x = -]]
10 10 5
Categories: Numerical methods · Share packages · Package simplex
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Default value: 10^-8
Epsilon used for numerical computations in linear_program.
See also: linear_program.
Categories: Package simplex
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_lp, scale_lp, and epsilon_lp.
Categories: Package simplex · Numerical methods
Maximizes linear objective function obj subject to some linear
constraints cond. See minimize_lp for detailed
description of arguments and return value.
See also: minimize_lp.
Categories: Package simplex · Numerical methods
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: maximize_lp, nonegative_lp, epsilon_lp.
Categories: Package simplex · Numerical methods
Default value: false
If nonegative_lp is true all decision variables to
minimize_lp and maximize_lp are assumed to be positive.
See also: minimize_lp.
Categories: Package simplex
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