fmincon: speed of linear equality- versus inequality-constrained optimization problems

Hello,

I have a question about the speed benefits of formulating a particular optimization problem in a way that involves linear equality constraints, or as one that involves linear inequality constraints. I am thinking of the fmincon algorithms.

My intuition is that linear equality constraints are typically easier/faster for fmincon to handle than linear inequality constraints. So, if it's possible to re-formulate an inequality-constrained problem as one that is equality-constrained, it seems this might have some speed benefits.

Of course, this depends on how the inequality-constrained problem is converted into an equality-constrained problem, and it probably depends on the scale of the problem.

Let's assume a fairly small problem, with a few dozen inequality constraints. To convert the inequality constraints into equality constraints, I would add a slack choice variable for each *inequality* constraint, and impose the corresponding *equality* constraint that a linear combination of the expanded set of choice variables is equal to the contraint.

Does this seem likely to have any performance benefits?

Thank you