# lagrangian: Solve lagrange multiplier problems

[ bsd3, library, math ] [ Propose Tags ]

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, 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 ad (==3.4.*), base (==4.6.*), hmatrix (==0.14.*), nonlinear-optimization (==0.3.*), vector (==0.10.*) [details] BSD-3-Clause Jonathan Fischoff jonathangfischoff@gmail.com Math http://github.com/jfischoff/lagrangian by JonathanFischoff at Sat Mar 9 17:58:51 UTC 2013 NixOS:0.6.0.1 3646 total (104 in the last 30 days) (no votes yet) [estimated by rule of succession] λ λ λ Docs uploaded by userBuild status unknown Hackage Matrix CI

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