Is there any known Poly-APX-complete minimimization problem?
I've just discovered there exists at least one confirmed minimization Poly-APX-complete problem: Min ones if setting all variables true satisfies all clauses (together with other conditions). It is shown in "The Approximability of Constraint Satisfaction
Problems" by Sanjeev Khannay, Madhu Sudanz, Luca Trevisanx and David P. Williamson (http://people.csail.mit.edu/madhu/papers/2001/kstw.pdf), Theorem 2.14, item (5).