67 lines
2.5 KiB
Markdown
67 lines
2.5 KiB
Markdown
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# fmin [](https://travis-ci.org/benfred/fmin)
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Unconstrained function minimization in javascript.
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This package implements some basic numerical optimization algorithms: Nelder-Mead, Gradient
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Descent, Wolf Line Search and Non-Linear Conjugate Gradient methods are all provided.
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Interactive visualizations with D3 explaining how these algorithms work are also included in this package.
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Descriptions of the algorithms as well as most of the visualizations are available on my blog post
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[An Interactive Tutorial on Numerical
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Optimization](http://www.benfrederickson.com/numerical-optimization/).
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## Installing
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If you use NPM, `npm install fmin`. Otherwise, download the [latest release](https://github.com/benfred/fmin/releases/latest).
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## API Reference
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<a href="#nelderMead" name="nelderMead">#</a> <b>nelderMead</b>(<i>f</i>, <i>initial</i>)
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Uses the [Nelder-Mead method](https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method) to
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minimize a function <i>f</i> starting at location <i>initial</i>.
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Example usage minimizing the function <i>f(x, y) = x<sup>2</sup> + y<sup>2</sup> + x sin y + y
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sin x</i> is:
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```js
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function loss(X) {
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var x = X[0], y = X[1];
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return Math.sin(y) * x + Math.sin(x) * y + x * x + y *y;
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}
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var solution = fmin.nelderMead(loss, [-3.5, 3.5]);
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console.log("solution is at " + solution.x);
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```
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<!--
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<a href="#gradientDescent" name="gradientDescent">#</a> <b>gradientDescent</b>()
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[](./examples/gradient_descent.html)
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-->
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<a href="#conjugateGradient" name="conjugateGradient">#</a> <b>conjugateGradient</b>(<i>f</i>, <i>initial</i>)
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Minimizes a function using the [Polak–Ribière non-linear conjugate gradient method
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](https://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method). The function <i>f</i> should
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compute both the loss and the gradient.
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An example minimizing [Rosenbrock's Banana
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function](https://en.wikipedia.org/wiki/Rosenbrock_function) is:
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```js
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function banana(X, fxprime) {
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fxprime = fxprime || [0, 0];
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var x = X[0], y = X[1];
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fxprime[0] = 400 * x * x * x - 400 * y * x + 2 * x - 2;
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fxprime[1] = 200 * y - 200 * x * x;
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return (1 - x) * (1 - x) + 100 * (y - x * x) * (y - x * x);
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}
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var solution = fmin.conjugateGradient(banana, [-1, 1]);
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console.log("solution is at " + solution.x);
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```
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