The lagrangian package

[Tags: bsd3, library]

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.


Properties

Versions0.1.0.0, 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
Dependenciesad (==3.4.*), base (==4.6.*), hmatrix (==0.14.*), nonlinear-optimization (==0.3.*), vector (==0.10.*)
LicenseBSD3
AuthorJonathan Fischoff
Maintainerjonathangfischoff@gmail.com
CategoryMath
Home pagehttp://github.com/jfischoff/lagrangian
Upload dateSun Mar 10 06:00:17 UTC 2013
Uploaded byJonathanFischoff
Downloads567 total (50 in last 30 days)

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