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

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
Dependencies ad (==4.*), base (>=4.5 && <5), hmatrix (>=0.14 && <0.17), nonlinear-optimization (==0.3.*), vector (==0.10.*) [details]
License BSD3
Author (c) Jonathan Fischoff 2012-2014, (c) Eric Pashman 2014
Maintainer jonathangfischoff@gmail.com
Stability Unknown
Category Math
Home page http://github.com/jfischoff/lagrangian
Uploaded Thu Oct 9 06:56:36 UTC 2014 by JonathanFischoff
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Downloads 1802 total (37 in the last 30 days)
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Status Docs uploaded by user
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