@hackage lagrangian0.4.0.0

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, 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.