If somebody has an experience in minimization where the problem has multiple minimizers.
1. Is it necessary to re-run the same subroutine to find next minimizer and so on, until all minimizers will be computed(one re-run - one minimizer)? If so, is it necessary to use as an input for the next re-run, minimizers, computed at the previous re-runs?
2. As a rule, the complexity of minimization is being evaluated per one minimizer. If per one minimizer its polynomial-time, what can we say about total complexity?