fmin

Unconstrained function minimization in javascript.

This package implements some basic numerical optimization algorithms: Nelder-Mead, Gradient Descent, Wolf Line Search and Non-Linear Conjugate Gradient methods are all provided.

Interactive visualizations with D3 explaining how these algorithms work are also included in this package. Descriptions of the algorithms as well as most of the visualizations are available on my blog post An Interactive Tutorial on Numerical Optimization.

Installing

If you use NPM, npm install fmin. Otherwise, download the latest release.

API Reference

# nelderMead(f, initial)

Uses the Nelder-Mead method to minimize a function f starting at location initial.

Example usage minimizing the function f(x, y) = x² + y² + x sin y + y sin x is:

function loss(X) {
    var x = X[0], y = X[1];
    return Math.sin(y) * x  + Math.sin(x) * y  +  x * x +  y *y;
}

var solution = fmin.nelderMead(loss, [-3.5, 3.5]);
console.log("solution is at " + solution.x);

# conjugateGradient(f, initial)

Minimizes a function using the Polak–Ribière non-linear conjugate gradient method . The function f should compute both the loss and the gradient.

An example minimizing Rosenbrock's Banana function is:

function banana(X, fxprime) {
    fxprime = fxprime || [0, 0];
    var x = X[0], y = X[1];
    fxprime[0] = 400 * x * x * x - 400 * y * x + 2 * x - 2;
    fxprime[1] = 200 * y - 200 * x * x;
    return (1 - x) * (1 - x) + 100 * (y - x * x) * (y - x * x);
}

var solution = fmin.conjugateGradient(banana, [-1, 1]);
console.log("solution is at " + solution.x);