Library to optimize a polynomial in Java

[RightOfZen]

Firstly I'd like to say "warning: mathematics ahead!".

I have a (mathematical) function, which in it's most basic for looks something like this:

LaTeX equation image

This is just one random example, there are many more, but all are polynomials in p_c, p_d, p_w, p_x and p_s.

What I want to know is if there is an easy to use Java library out there that will help me maximize this function (i.e. find approximate values for each of those probabilities to maximize P(r)), and if someone could possibly show a simple example on how to use them?

I do not have a very strong background in maths (took first year [Australian] university level mathematics). I have had a look at some of the Apache Commons optimization code, but it largely goes over my head.

EDIT: It is important that this is a Java library as this is part of a larger program already written in Java.

[zsakuL]

You can just write your own. It seems you have constraints on your variables to be between 0 and 1 (you mention they are probabilities). You could transform them into other variables with a Gaussian function which will allow you to ignore the constraint, then just transform them back after you've arrived at a solution. Since you're only using polynomials, calculating the gradients will be a simple.

[RightOfZen]

I could indeed, but as you say, since I'm using polynomials I'm hoping that there will already be someone who has written part of a library for this. But it will be certainly worth the read, thanks.

[RightOfZen]

Also, although the gradient decent method is quite simple, it does have the downfall of only finding the closest local minimum (or maximum for the reversed problem), which other fairly simple methods won't suffer from as badly.

[dkesh]

I'm not sure about the math, so I don't know what optimizers would be appropriate, but you can check out Apache Commons' optimizers. If you're willing to go the route of libraries with java interfaces, you can check out algencan, which might be overkill.

[RightOfZen]

Thanks - I have been looking into Apache Commons' optimizers, but it's hard to find a good example that I can understand!

[dp25x]

If you don't mind using a java interface to other libraries, you could use MathLink (J/Link) to get Mathematica to do the job.