On the extreme points of moments sets

Iosif Pinelis ()
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Iosif Pinelis: Michigan Technological University

Mathematical Methods of Operations Research, 2016, vol. 83, issue 3, No 2, 325-349

Abstract: Abstract Necessary and sufficient conditions for a measure to be an extreme point of the set of measures on a given measurable space with prescribed generalized moments are given, as well as an application to extremal problems over such moment sets; these conditions are expressed in terms of atomic partitions of the measurable space. It is also shown that every such extreme measure can be adequately represented by a linear combination of k Dirac probability measures with nonnegative coefficients, where k is the number of restrictions on moments; moreover, when the measurable space has appropriate topological properties, the phrase “can be adequately represented by” here can be replaced simply by “is”. Applications to specific extremal problems are also given, including an exact lower bound on the exponential moments of truncated random variables, exact lower bounds on generalized moments of the interarrival distribution in queuing systems, and probability measures on product spaces with prescribed generalized marginal moments.

Keywords: Moment sets; Measures; Generalized moments; Extreme points; Optimization; Extremal problems; Atoms; Convex sets; Queuing systems; Primary 49K30; 49K27; 52A40; Secondary 26D15; 46A55; 46N10; 46N30; 60B05; 60K25; 90B22; 90C05; 90C25; 90C26; 90C48 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00186-015-0530-0

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