Originally posted by: BerkUstun

Say that I have an LP of the form

min  cx
s.t. Ax = b
     lb <= x <= ub

CPLEX allows me to incorporate the box constraints (i.e. lb <= x <= ub) in two different ways.

1) I can include these as constraints within the "A" matrix

2) I can include these as values within the "lb" and "ub" fields of each column.

I'm wondering if it makes a difference to choose approach 1) over approach 2) when I solve an LP using the default settings in CPLEX.

Do all the lb/ub constraints eventually end up in the A matrix? Or are they used in a clever way (i.e. I know that there is a variant of the Simplex algorithm that can exploit box constraints to speed up convergence).
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Originally posted by: T_O

When preprocessing is enabled, it should not make any difference because CPLEX will convert the constraints into bounds.

However, if preprocessing is disabled, it should make a difference. CPLEX uses clever primal and dual simplex algorithms that respect bounds. Remember for example that problems where all variables are bounded are always dual feasible.

In doubt, I would always use bounds instead of constraints.

Best regards,
Thomas
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Originally posted by: BerkUstun

Thank you for a thorough answer!
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