About bounds

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Oct 23, 2023, 10:34:45 AM10/23/23
to Artelys Knitro forum
Hi there

I want to check something about setting bounds on my variables and how it would affect the solver.

I have the following constraint:
LB <= x1 <= x2 <= ... <= xn <= UB

The constraints x1 <= x2 <= ... <= xn I set as linear constraints, whereas LB and UB I place as bounds on the variables.

My question is, how should I apply the bounds (and why)?: 
to all variables (LB <= x1,x,2,..xn <= UB), or
only at the boundaries (LB <= x1 and xn <= UB)

I guess the option (LB <= x1,x,2,..xn <= UB) would be redundant?

Thank you, and kind regards

Richard Waltz

Oct 23, 2023, 10:47:37 AM10/23/23
to Artelys Knitro forum

I would suggest only adding the necessary bounds (LB <= x1 and xn <= UB) and not the redundant bounds.  As a general modeling rule, at least with continuous problems, it is usually best to define the problem using the minimal set of constraints necessary to accurately model the problem.  Adding redundant/unnecessary constraints can often make the problem harder to solve (usually the Knitro presolver will just remove the redundant bounds/constraints by default anyway).  If you are providing an initial point, however, I would recommend specifying an initial value for all x1,x,2,..xn that is between LB and UB.

-Richard Waltz

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