The Simplex Algorithm and beyond….
In practice, quite fast -- typically only O(m) pivots (where m is the number of constraints)
In worst case, exponential.
For a long time, it wasn’t known if there was a polynomial time algorithm until….
Khachian’s algorithm “The Mathematical Sputnik of 1979”
And then there was Karmakar (1984)…
- interior-point method
- competes viably with simplex algorithm on real-world problems.