Simplex Algorithm

[ftneek]

I agree, with only 1 pivot changing each iteration we can save a lot of operations. But I think in the beginning it still needs to go over each pivot at least once, and then the rest of the time it can pivot as you suggest. The reason is because simplex_core accepts a system in canonical or standard form. If it is standard form, I think it needs the pivots. For example for ">=" constraints you can just add negative slack variables if you pivot on them and use dual simplex, which is equivalent to multiplying the constraint by -1 and adding slack variable. Artificial variables also require a pivot, as well as choosing non slack/artificial as initial bv.

I still need to look over the other changes to see how it could have an effect. I will just say I probably prefer artificial variables to be set up outside of simplex_core. It can't be done inside of simplex? Or if you make it another function, it would probably be useful in a program for converting from symbolic input to standard form.