On minquantile and maxcovering optimisation

On minquantile and maxcovering optimisation

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Article ID: iaor19971127
Country: Netherlands
Volume: 71
Issue: 1
Start Page Number: 101
End Page Number: 112
Publication Date: Nov 1995
Journal: Mathematical Programming (Series A)
Authors: ,
Keywords: decision theory: multiple criteria
Abstract:

In this paper the authors introduce the parametric minquantile problem, a weighted generalisation of kth maximum minimisation. It is shown that, under suitable quasiconvexity assumptions, its resolution can be reduced to 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 the covering and minimize the cover-level, are reducible to a discrete problem, on which any multiple criteria method may be applied.

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