Stability | provisional |
---|---|

Maintainer | Alberto Ruiz (aruiz at um dot es) |

Safe Haskell | Safe-Infered |

This module provides an interface to the standard simplex algorithm.

For example, the following LP problem

maximize 4 x_1 - 3 x_2 + 2 x_3 subject to 2 x_1 + x_2 <= 10 x_3 + 5 x_4 <= 20 and x_i >= 0

can be solved as follows:

import Numeric.LinearProgramming prob = Maximize [4, -3, 2] constr1 = Sparse [ [2#1, 1#2] :<=: 10 , [1#2, 5#3] :<=: 20 ] > simplex prob constr1 [] Optimal (28.0,[5.0,0.0,4.0])

The coefficients of the constraint matrix can also be given in dense format:

constr2 = Dense [ [2,1,0] :<=: 10 , [0,1,5] :<=: 20 ]

By default all variables are bounded as `x_i >= 0`

, but this can be
changed:

> simplex prob constr2 [ 2 :=>: 1, 3 :&: (2,7)] Optimal (22.6,[4.5,1.0,3.8]) > simplex prob constr2 [Free 2] Unbounded

The given bound for a variable completely replaces the default,
so `0 <= x_i <= b`

must be explicitly given as `i :&: (0,b)`

.
Multiple bounds for a variable are not allowed, instead of
`[i :=>: a, i:<=: b]`

use `i :&: (a,b)`

.

- simplex :: Optimization -> Constraints -> Bounds -> Solution
- data Optimization
- data Constraints
- type Bounds = [Bound Int]
- data Bound x
- (#) :: Double -> Int -> (Double, Int)
- data Solution