# The Multidimensional Moment Problem with Complexity Constraint

arXiv: https://arxiv.org/abs/1504.03626 · HTML: https://mlsanity.com/paper/1504.03626/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2015.

## Built on by (most cited first, 1 of 1)

- [A Non-Classical Parameterization for Density Estimation Using Sample Moments](https://mlsanity.com/paper/2201.04786/) (2022)

## Abstract (arXiv)

A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the solution set in terms of a bounded finite number of parameters is required. In this paper we provide a complete solution of the multidimensional moment problem with a complexity constraint also allowing for solutions that require a singular measure added to the rational, absolutely continuous one. Such solutions occur on the boundary of a certain convex cone of solutions. In this paper we provide complete parameterizations of all such solutions. We also provide errata for a previous paper in this journal coauthored by one of the authors of the present paper.