Solve Lagrange multiplier problems http://github.com/jfischoff/lagrangian
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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.