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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.
