Stability and convergence

The algorithms used to solve linear programming problems are all forced to make an assumption: that tiny changes to the system (e.g., making a small step in barrier) lead to small changes in the solution. If this is not true (due to ill-conditioning), then the algorithm may jump around in the solution space and have a hard time converging.

Finally, one way to improve the geometry of a problem is by suitably scaling variables and constraints as explained in the Scaling section, and working with bounded feasible sets with reasonable ranges for all variables.