Total number of variables does not add up

[Pagnon David]

Hello,

When running IPOPT within Moco, it seems like the number of variables does not add up. Could you help me understand it?

Code: Select all

Total number of variables............................:    22913
                     variables with only lower bounds:        0
                variables with lower and upper bounds:    22172
                     variables with only upper bounds:        0
Total number of equality constraints.................:    20152
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

Thank you!

[Nicholas Bianco]

Hi David,

This means that there are some variables in the problem that do not have any bounds set for them. These could be variables in the Moco problem, or slack variables added by Ipopt.

Best,
Nick

[Pagnon David]

Thanks, it makes sense!

[Pagnon David]

Hi,

I'm still definitely a beginner at Moco and NLP in general, so please excuse my potentially naive questions.

I'm looking at the Moco objective function and the constraints it is subject to, as well as the output posted above.

I am wondering, what are some variables that would typically not have any lower nor upper bounds?

And what is the rationale behind the fact that the number of variables is slightly larger than the number of equality constraints? I guess that the constraints involve most variables but not all of them. Which ones would not be constrained?

Thanks in advance! If this is not clear, I can probably think a bit more and reformulate it.

[Nicholas Bianco]

Hi David,

All questions are welcome!

Any variables that you do not provide bounds for will not have bounds in the IPOPT optimization problem. Moco automatically sets bounds for most variables based on ranges set in the model, but this sometimes doesn't catch all variables. Also, I misspoke before, IPOPT does introduce additional "slack" variables in optimization problems, but I do not think that are counted in the problem output you see.

The number of variables is not necessarily the same (and typically is not) the same as the number of equality constraints in the problem. Note that IPOPT treats simple variable bounds differently than other constraints in the problem. Furthermore, since bounds are usually less than/greater than constraints, they wouldn't show up in the equality constraint count anyway.

Hopefully this is helpful.

Best,
Nick