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

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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.

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Acknowledgments

This research was supported by NSF grant CMMI-0856663.

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Authors and Affiliations

  1. Rutgers Center of Operations Research, Rutgers University, New Brunswick, NJ, USA

    András Prékopa

  2. Department of Mathematics, College of William and Mary, Williamsburg, VA, USA

    Anh Ninh

  3. Dana-Farber Cancer Institute, Boston, MA, USA

    Gabriela Alexe

  4. Harvard Medical School, Boston, MA, USA

    Gabriela Alexe

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Prékopa, A., Ninh, A. & Alexe, G. On the relationship between the discrete and continuous bounding moment problems and their numerical solutions. Ann Oper Res 238, 521–575 (2016). https://doi.org/10.1007/s10479-015-1995-1

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