numeric-optimization

Unified interface to various numerical optimization algorithms.

The aim of the package is to provide a convenient interface like Python's scipy.optimize.

Note that the package name is numeric-optimization and not numerical-optimization. The name numeric-optimization comes from the module name Numeric.Optimization.

Example Usage

{-# LANGUAGE OverloadedLists #-}
import Data.Vector.Storable (Vector)
import Numeric.Optimization

main :: IO ()
main = do
  result <- minimize LBFGS def (WithGrad rosenbrock rosenbrock') [-3,-4]
  print (resultSuccess result)  -- True
  print (resultSolution result)  -- [0.999999999009131,0.9999999981094296]
  print (resultValue result)  -- 1.8129771632403013e-18

-- https://en.wikipedia.org/wiki/Rosenbrock_function
rosenbrock :: Vector Double -> Double
rosenbrock [x,y] = sq (1 - x) + 100 * sq (y - sq x)

rosenbrock' :: Vector Double -> Vector Double
rosenbrock' [x,y] =
  [ 2 * (1 - x) * (-1) + 100 * 2 * (y - sq x) * (-2) * x
  , 100 * 2 * (y - sq x)
  ]

sq :: Floating a => a -> a
sq x = x ** 2

Supported Algorithms

Algorithm	Solver implemention	Haskell binding
CG_DESCENT	CG_DESCENT-C	nonlinear-optimization	Requires with-cg-descent flag
Limited memory BFGS (L-BFGS)	liblbfgs	lbfgs
Limited memory BFGS with bounds constraints (L-BFGS-B)	L-BFGS-B	l-bfgs-b	Requires with-lbfgsb flag
Newton's method	Pure Haskell implementation using HMatrix	-

Installation

Installing Prerequisites

BLAS and LAPACK

You may need to install BLAS and LAPACK for hmatrix.

Windows (MSYS2):

$ pacman -S mingw-w64-x86_64-lapack

or if you use MSYS2 installed by stack

$ stack exec -- pacman -S mingw-w64-x86_64-lapack

Debian and Ubuntu Linux:

$ apt-get install libblas-dev liblapack-dev

libblas-dev and liblapack-dev are reference implementations. You need to install optimized ones for better performance. (See DebianScience/LinearAlgebraLibraries)

macOS

By default hmatrix uses BLAS and LAPACK provided by Accelerate Framework provided by macOS.

liblbfgsb

If you want to use L-BFGS-B, you have to install the development package of liblbfgsb.

Ubuntu Linux:

$ apt-get install liblbfgsb-dev

Homebrew (macOS and Linux):

$ brew install msakai/tap/liblbfgsb

Windows (MSYS2):

$ wget https://github.com/msakai/mingw-w64-liblbfgsb/releases/download/v3.0-1/mingw-w64-x86_64-liblbfgsb-3.0-1-any.pkg.tar.zst
$ pacman -U mingw-w64-x86_64-liblbfgsb-3.0-1-any.pkg.tar.zst

or if you use MSYS2 installed by stack

$ wget https://github.com/msakai/mingw-w64-liblbfgsb/releases/download/v3.0-1/mingw-w64-x86_64-liblbfgsb-3.0-1-any.pkg.tar.zst
$ stack exec -- pacman -Sy
$ stack exec -- pacman -U mingw-w64-x86_64-liblbfgsb-3.0-1-any.pkg.tar.zst

Related Packages

• Packages for using with automatic differentiation:
  • numeric-optimization-ad for using with ad package
  • numeric-optimization-backprop for using with backprop package
• MIP for solving linear programming and mixed-integer linear programming problems

LICENSE

The code in thie packaged is licensed under BSD-3-Clause.

If you enable with-cg-descent flag, it uses GPL-licensed packages and the resulting binary should be distributed under GPL.