# POP

## Seminar

### The A-Truncated K-Moment Problem

Seminar Room 1, Newton Institute

#### Abstract

Let A be a finite subset of N^n, and K be a compact semialgebraic set. An A-tms is a vector y indexed by elements in A. The A-Truncated K-Moment Problem (A-TKMP) studies whether a given A-tms y admits a K-measure(i.e., a Borel measure supported in K) or not. We propose a numerical algorithm for solving A-TKMPs. It is based on finding a flat extension of y by solving a hierarchy of semidefinite relaxations, whose objective R is generated in a certain randomized way. If y admits no K-measures and R[x]_A is K-full, we can get a certificate for the nonexistence of representing measures. If y admits a K-measure, then for almost all generated R, we prove

that: i) we can asymptotically get a flat extension of y; ii) under a general condition that is almost sufficient and necessary, we can get a flat

extension of y. The complete positive matrix decomposition and sum of even powers of linear forms decomposition problems can be solved as an A-TKMP.

#### Video

**The video for this talk should appear here if JavaScript is enabled.**

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.