ON MINQUANTILE AND MAXCOVERING OPTIMIZATION

In this paper we introduce the parametric minquantile problem, a weigh ted generalisation of kth maximum minimisation. It is shown that, unde r suitable quasiconvexity assumptions, its resolution can be reduced t o solving a polynomial number of minmax problems. It is also shown how this simultaneously solves (parametric) maximal covering problems. It follows that bicriteria problems, where the aim is to both maximize t he covering and minimize the cover-level, are reducible to a discrete problem, on which any multiple criteria method may be applied.