Hi the solution with linear programming works very well! Even if I take more 'realistic' matrices with dimensions of about 25x60, the calculation of the basis goes well (if I increase the number of iterations to 1000). Meanwhile I also found an algorithm for an exact calculation of the extreme rays of the cone (Appendix in http://www.sciencedirect.com/science/article/pii/S0022519300910737). When I have time I will try to implement this solution as well and compare the performances, but the one I have now works fine in my application. Many thanks, Hannes
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