lagrangian

Solve Lagrange multiplier problems

http://github.com/jfischoff/lagrangian

Latest on Hackage:0.6.0.1

This package is not currently in any snapshots. If you're interested in using it, we recommend adding it to Stackage Nightly. Doing so will make builds more reliable, and allow stackage.org to host generated Haddocks.

BSD-3-Clause licensed by (c) Jonathan Fischoff 2012-2014, (c) Eric Pashman 2014
Maintained by [email protected]

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.