Numeric.GSL.Minimization
 Portability uses ffi Stability provisional Maintainer Alberto Ruiz (aruiz at um dot es)
Description

Minimization of a multidimensional function using some of the algorithms described in:

The example in the GSL manual:

```
f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30

main = do
let (s,p) = minimize NMSimplex2 1E-2 30 [1,1] f [5,7]
print s
print p

> main
[0.9920430849306288,1.9969168063253182]
0.000  512.500  1.130  6.500  5.000
1.000  290.625  1.409  5.250  4.000
2.000  290.625  1.409  5.250  4.000
3.000  252.500  1.409  5.500  1.000
...
22.000   30.001  0.013  0.992  1.997
23.000   30.001  0.008  0.992  1.997
```

The path to the solution can be graphically shown by means of:

`Graphics.Plot.mplot \$ drop 3 (toColumns p)`

Taken from the GSL manual:

The vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is a quasi-Newton method which builds up an approximation to the second derivatives of the function f using the difference between successive gradient vectors. By combining the first and second derivatives the algorithm is able to take Newton-type steps towards the function minimum, assuming quadratic behavior in that region.

The bfgs2 version of this minimizer is the most efficient version available, and is a faithful implementation of the line minimization scheme described in Fletcher's Practical Methods of Optimization, Algorithms 2.6.2 and 2.6.4. It supercedes the original bfgs routine and requires substantially fewer function and gradient evaluations. The user-supplied tolerance tol corresponds to the parameter sigma used by Fletcher. A value of 0.1 is recommended for typical use (larger values correspond to less accurate line searches).

The nmsimplex2 version is a new O(N) implementation of the earlier O(N^2) nmsimplex minimiser. It calculates the size of simplex as the rms distance of each vertex from the center rather than the mean distance, which has the advantage of allowing a linear update.

Synopsis
minimize :: MinimizeMethod -> Double -> Int -> [Double] -> ([Double] -> Double) -> [Double] -> ([Double], Matrix Double)
data MinimizeMethod
 = NMSimplex | NMSimplex2
minimizeD :: MinimizeMethodD -> Double -> Int -> Double -> Double -> ([Double] -> Double) -> ([Double] -> [Double]) -> [Double] -> ([Double], Matrix Double)
data MinimizeMethodD
 = ConjugateFR | ConjugatePR | VectorBFGS | VectorBFGS2 | SteepestDescent
minimizeNMSimplex :: ([Double] -> Double) -> [Double] -> [Double] -> Double -> Int -> ([Double], Matrix Double)
minimizeConjugateGradient :: Double -> Double -> Double -> Int -> ([Double] -> Double) -> ([Double] -> [Double]) -> [Double] -> ([Double], Matrix Double)
minimizeVectorBFGS2 :: Double -> Double -> Double -> Int -> ([Double] -> Double) -> ([Double] -> [Double]) -> [Double] -> ([Double], Matrix Double)
Documentation
 minimize Source
 :: MinimizeMethod -> Double desired precision of the solution (size test) -> Int maximum number of iterations allowed -> [Double] sizes of the initial search box -> [Double] -> Double function to minimize -> [Double] starting point -> ([Double], Matrix Double) solution vector and optimization path Minimization without derivatives.
 data MinimizeMethod Source
Constructors
 NMSimplex NMSimplex2 Instances
 Bounded MinimizeMethod Enum MinimizeMethod Eq MinimizeMethod Show MinimizeMethod
 minimizeD Source
 :: MinimizeMethodD -> Double desired precision of the solution (gradient test) -> Int maximum number of iterations allowed -> Double size of the first trial step -> Double tol (precise meaning depends on method) -> [Double] -> Double function to minimize -> [Double] -> [Double] gradient -> [Double] starting point -> ([Double], Matrix Double) solution vector and optimization path Minimization with derivatives.
 data MinimizeMethodD Source
Constructors
 ConjugateFR ConjugatePR VectorBFGS VectorBFGS2 SteepestDescent Instances
 Bounded MinimizeMethodD Enum MinimizeMethodD Eq MinimizeMethodD Show MinimizeMethodD
 minimizeNMSimplex :: ([Double] -> Double) -> [Double] -> [Double] -> Double -> Int -> ([Double], Matrix Double) Source
 minimizeConjugateGradient :: Double -> Double -> Double -> Int -> ([Double] -> Double) -> ([Double] -> [Double]) -> [Double] -> ([Double], Matrix Double) Source
 minimizeVectorBFGS2 :: Double -> Double -> Double -> Int -> ([Double] -> Double) -> ([Double] -> [Double]) -> [Double] -> ([Double], Matrix Double) Source