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September 27th, 2011, 09:17 PM   #1
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"combinatorial" linear equation systems

I'm looking for a possible method if it exists at all to solve my problem:

Please see http://en.wikipedia.org/wiki/System_of_ ... x_equation as I'm going to reference the naming.

For Matrix A I have lets say there are x possible "columns". however for any solution I only want to use y of those x columns (x is around 1000 and y 20-50).

A second problem is that a solution is only applicable (has meaning) if all x1...xn in the solution vector are a) between 0 and 1 b) their sum is between 0 and 1.

Of course that leads to a very, very large amount of combinations to "test". Is there any known method for such a problem?
(it will be solved in a computer). Brute force does not seem to be an option since for x=1000 and y = 40, I get something like 5.6*10^71 combinations...if you also consider that 21,22,23,24,...50 are also valid y...

Any Ideas?
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