Golden Section Search for node.js. A line search technique used to minimize or maximize the output a function, also known as `argmax`.
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Golden Section Search

A line search technique to help you find the minimum or maximum of a function. I've adapted the version from wikipedia to support async functions as well as synchronous ones :)

How to use

npm install gss

The arguments are a bit bad, but here's how you'd use it:

gss(asyncFunctionToMinimize, lowerBound, middleNumber, upperBound, precision, callback(err, min))
  • asyncFunctionToMinimize(x, cb): takes one argument, x, for which you are finding the argmax, and a callback that it calls when finished. It should call its callback like this: cb(null, result).
  • lowerBound: a number you think makes a lower bound to the solution
  • middleNumber: any number between the upper and lower bounds
  • upperBound: a number you think makes an upper bound to the solution
  • callback(err, min): a function to receive the results of the line search

The synchronous version takes a function that returns the result, and when it finishes it returns the result, so you don't need a callback. See the example below.

Async example:

var gss = require('gss').gss

// f(x) = x^2
var f = function(x, cb) { cb(null, Math.pow(x, 2)); } 

gss(f, -10, -7, 1, Math.sqrt(1e-10), function(err, min) {
  // Now we have the min!
  console.log(min, 'this should be prettty close to zero.');

Sync example (you bad bad noder ;):

  var gssSync = require('gss').gssSync
  var f = function(x) { return Math.pow(x, 2); } // f(x) = x^2

  var min = gssSync(_.memoize(f), -100, -50, 100, Math.sqrt(1e-10))
  console.log(min, 'should be pretty darn close to zero.');


I recommend you use _.memoize to make the minimization go as quickly as possible. If you'd like to maximize instead, have your function multiply by -1 before returning.


  • tests
  • automatically choose the middleNumber, to simplify API