Continuity and monotonicity of solutions to a greedy maximization problem

Łukasz Kruk ()
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Łukasz Kruk: Maria Curie-Skłodowska University

Mathematical Methods of Operations Research, 2020, vol. 92, issue 1, No 2, 33-76

Abstract: Abstract Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $${\mathbb {R}}^n$$ R n , with the admissible set indexed by the time parameter. The structure of the constraints depends on the underlying network topology. We investigate continuity and monotonicity of the resulting maximizers with respect to time. Our results have important consequences for fluid models of the corresponding networks which are optimal, in the appropriate sense, with respect to handling real-time transmission requests.

Keywords: Partial order; Greedy maximization; Continuity; Monotonicity; Resource sharing; Fluid model; 06A06; 26A15; 26A48; 68M20; 90B10; 90C35 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-020-00705-x

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