On the relationship between the discrete and continuous bounding moment problems and their numerical solutions

András Prékopa (), Anh Ninh () and Gabriela Alexe
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András Prékopa: Rutgers University
Anh Ninh: College of William and Mary
Gabriela Alexe: Boston

Annals of Operations Research, 2016, vol. 238, issue 1, No 23, 575 pages

Abstract: Abstract We present a brief survey of some of the basic results related to the classical continuous moment problems (CMP) and the recently developed discrete moment problems (DMP), clarifying their relationship and propose new methods for the solution of univariate continuous and discrete power moment problems. In the classical as well as in the recently developed discrete moment problems the coefficient function in the objective is supposed to be higher order convex (in the entire interval or part of it), or constant in an interval while zero elsewhere, or equal to a constant at some point and zero elsewhere. The concept of a regenerative block (of points) is introduced, for the case of the DMP, that makes it possible to create lower and upper bounds for other functions in the objective. The CMP are solved by discretization and sequential application of dual type algorithm. Numerical results are presented with moments of order up to 40 and various applications are mentioned.

Keywords: Moment problems; Semi-infinite linear programs; Discrete moment problems; Bounding probabilities and expectations (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10479-015-1995-1

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