README.md

A Nelder-Mead implementation in Go

The Go package documentation has in-depth usage help and algorithm tuning suggestions. This package intends to be super easy to use and optimize.

This repository contains a Go implementation of the Nelder-Mead optimization algorithm, which is a gradient-free optimization method for continuous, possibly non-convex, and noisy functions in low to moderate dimensions.

The algorithm uses a simplex, a polytope with n+1 vertices in n-dimensional space, to explore the search space. The algorithm iteratively updates the simplex by reflecting, expanding, contracting, or shrinking it, based on the values of the objective function at its vertices. The algorithm terminates when the difference in the objective function values between the best and worst points in the simplex falls below the specified tolerance or when the maximum number of iterations is reached.

Installation

This package can be installed using Go modules with the following command:

go get github.com/crhntr/neldermead

Usage

Try it in the Go playground

The Rosenbrock function is a well-known test function for optimization algorithms, and its global minimum is at (1, 1), where the function value is 0. The Run function takes the Rosenbrock function as the objective function to minimize, the initial guess x0 as the starting point, and the Options struct with the desired parameters for the Nelder-Mead algorithm.

The algorithm found a solution close to the global minimum with a very small objective function value.

package main

import (
	"fmt"
	"math"

	"github.com/crhntr/neldermead"
)

func main() {
	rosenbrock := func(x []float64) float64 {
		return math.Pow(1-x[0], 2) + 100*math.Pow(x[1]-x[0]*x[0], 2)
	}
	x0 := []float64{-1, -1} // initial guess
	options := neldermead.NewOptions()

	point, err := neldermead.Run(rosenbrock, x0, options)
	if err != nil {
		fmt.Printf("Error: %v\n", err)
	}
	fmt.Printf("Solution: %.6f\n", point.X)
	fmt.Printf("Objective function value: %.6f\n", point.F)
}

The output of this program should be:

Solution: [1.000329 1.000714]
Objective function value: 0.000000

Now let's look at an example with constraints,

package main

import (
	"fmt"
	"math"
	
	"github.com/crhntr/neldermead"
)

func main() {
	// Define the objective function to be minimized.
	objective := func(x []float64) float64 {
		// y = x^3
		return math.Pow(x[0], 3) - x[1]
	}

	// Define the starting point for the optimizer.
	x0 := []float64{4, 5}

	// Define the optimization options.
	options := neldermead.NewOptions()
	// (optional) add constraints
	options.Constraints = []neldermead.Constraint{
		{Min: 3, Max: 5},
		{Min: 0, Max: 10},
	}

	// Run the optimizer.
	result, err := neldermead.Run(objective, x0, options)
	if err != nil {
		panic(err)
	}

	fmt.Printf("Found minimum at x = %v, f(x) = %.2f\n", result.X, result.F)
}

The output of this program should be:

Found minimum at x = [3 10], f(x) = 17.00