# lagrangian: Solve Lagrange multiplier problems

Numerically solve convex Lagrange multiplier problems with conjugate gradient descent.

For some background on the method of Lagrange multipliers checkout the wikipedia page http://en.wikipedia.org/wiki/Lagrange_multiplier

Here is an example from the Wikipedia page on Lagrange multipliers Maximize f(x, y) = x + y, subject to the constraint x^2 + y^2 = 1

> maximize 0.00001 (\[x, y] -> x + y) [(\[x, y] -> x^2 + y^2) <=> 1] 2 Right ([0.707,0.707], [-0.707])

For more information look here: http://en.wikipedia.org/wiki/Lagrange_multiplier#Example_1

For example, to find the maximum entropy with the constraint that the probabilities sum to one.

> maximize 0.00001 (negate . sum . map (\x -> x * log x)) [sum <=> 1] 3 Right ([0.33, 0.33, 0.33], [-0.09])

The first elements of the result pair are the arguments for the objective function at the maximum. The second elements are the Lagrange multipliers.

Versions | 0.1.0.0, 0.2.0.0, 0.2.0.1, 0.2.0.2, 0.3.0.0, 0.3.0.1, 0.4.0.0, 0.4.0.1, 0.5.0.0, 0.6.0.0, 0.6.0.1 |
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Dependencies | ad (==3.4.*), base (==4.6.*), hmatrix (==0.14.*), nonlinear-optimization (==0.3.*), vector (==0.10.*) [details] |

License | BSD-3-Clause |

Author | Jonathan Fischoff |

Maintainer | jonathangfischoff@gmail.com |

Category | Math |

Home page | http://github.com/jfischoff/lagrangian |

Uploaded | by JonathanFischoff at Wed Mar 13 02:30:24 UTC 2013 |

Distributions | NixOS:0.6.0.1 |

Downloads | 3690 total (18 in the last 30 days) |

Rating | (no votes yet) [estimated by rule of succession] |

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Status | Docs uploaded by user Build status unknown [no reports yet] Hackage Matrix CI |

## Downloads

- lagrangian-0.5.0.0.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)