The lagrangian package

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 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

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
Dependencies	ad (==3.4.), base (==4.6.), hmatrix (==0.14.), nonlinear-optimization (==0.3.), vector (==0.10.*)
License	BSD3
Author	Jonathan Fischoff
Maintainer	jonathangfischoff@gmail.com
Category	Math
Home page	http://github.com/jfischoff/lagrangian
Upload date	Wed Mar 13 02:30:24 UTC 2013
Uploaded by	JonathanFischoff
Downloads	468 total (38 in last 30 days)

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