performance differences in linprog optimization depending on how boundaries are incorporated

I had noticed a performance difference in linprog (large-scale) when incorporating boundary conditions into (lb;ub) vs just incorporating them in into the inequality matrix A by augmenting it with a sparse identity matrix (assuming lb). Expressing the bounds on x in the bounary variables seeems to converge faster. Can you please explain this performance difference? Thanks in advance.

Answer 1

[Alan Weiss]

Linear programming algorithms have a much easier time satisfying bounds than they do satisfying linear inequalities, so I am not at all surprised that there is a performance difference. Take a look at the linear programming algorithms to see how they work.

This observation is more general than linear programming. The documentation advises that you use the simplest constraint type possible, and it is explicit about what "simplest" means.

Alan Weiss

MATLAB mathematical toolbox documentation

[Ryan Alder]

Thank you. The documents you referenced are quite practical.