I am working with the LinearProgramming to solve my problem. I am using Simplex and RevisedSimplex methods. They are giving me drastically different results for the same parameters. Examples are attached as plots. Generally solutions are also different from expected. It is rather not a problem in my code, have checked it many times. It is all probably because of accuracy issues - I have constraints like:
... = ~ 10^(-62)
This is something I cannot avoid since I work on a strictly derived scientific model. Is there any way to overcome my problems? If not Mathematica, maybe there are some other packages for LP known for much higher precision? In one paper I have found analogous problem solved with Mathematica's LP which must have operated with the same range of precision as in my case (10^(-62)).
Thanks for suggestions.