User - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T03:03:18Z http://mathoverflow.net/feeds/user/31361 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/121536/efficient-algorithm-finding-a-solution-of-system-of-linear-inequalities/121538#121538 Answer by unknown (google) for Efficient algorithm finding 'a' solution of system of linear inequalities unknown (google) 2013-02-11T23:38:29Z 2013-02-11T23:38:29Z <p>You can use a genetic algorithm (very fast in this kind of problems) <a href="http://en.wikipedia.org/wiki/Genetic_algorithm" rel="nofollow">http://en.wikipedia.org/wiki/Genetic_algorithm</a> The possible DNA is a sequence of the binary representation of 40 float numbers. One evaluation criteria you can use is the uniform error of all inequalities. So, you will find 'a' solution of your problem if the evaluation of the best individual is zero. Of course this is the lazy method, it just works! You can try to solve this using a linear program, but i can't tell you if 600 inequalities and 40 dimensions will be solved very fast with a simple LP-solver.</p>