They clearly ask for the following
Condition for Use: This software is freely available, but we expect that all publications describing work using this software , or all commercial products using it, quote at least one of the references given below.
here https://users.iems.northwestern.edu/%7Enocedal/lbfgsb.html
This would indicate to me that it is not sufficient to cite LBFGSB.jl and thus mentioning their work indirectly or Optimization.jl that may wrap it for example.
They clearly ask for the following
here https://users.iems.northwestern.edu/%7Enocedal/lbfgsb.html
This would indicate to me that it is not sufficient to cite LBFGSB.jl and thus mentioning their work indirectly or Optimization.jl that may wrap it for example.