I needed to perform an optimization run of the form:
In this case f(x) and g(x) were having different units and different magnitudes. In that case it is better to solve first:
This will get a (hopefully) better spread of the λ’s. See: http://yetanothermathprogrammingconsultant.blogspot.com/2010/02/efficient-frontiers-in-mip-models.html.
Of course if λ=0 or λ=1 is part of the λ’s we need to trace, then this actually does not require extra models to solve, just a different ordering: first do λ=0 and λ=1 to get f0 and g0 and then do the λ’s in between. As the λ’s are user specified, we needed a little bit of logic to handle this.