May 2015 Archives

The Tripods Are Here!

Last time we discussed the polytope method, a multivariate function minimisation algorithm that seeks out a local minimum by stepping away from the worst of a set of points, most commonly a simplex; the multivariate generalisation of a triangle.

We got as far as implementing an algorithm for generating regular simplices of any size and location with ak.simplex and in this post we shall finish the job.

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The Tripods Are Coming!

Some time ago we took a first look at multivariate function minimisation in which we try to find a point at which a two or more argument function has a local minimum, or in other words a point at which it returns a value no greater than it does at any nearby points.
The approach that we took was that of a blindfolded hill climber; take a tentative step in some direction and if it leads to a better place commit to it, otherwise stay where you are and try again. Our ak.blindfoldMinimum implemented the simplest of such hill climbing algorithms, choosing each trial step at random. We concluded that we should do much better if we chose those steps more intelligently and in this post we shall do just that.

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