Algebraic boundary of matrices of nonnegative rank at most three

Research output: Contribution to journalArticleScientificpeer-review

Details

Original languageEnglish
Pages (from-to)62-80
Number of pages19
JournalLinear Algebra and Its Applications
Volume508
Publication statusPublished - 1 Nov 2016
MoE publication typeA1 Journal article-refereed

Researchers

Research units

  • University of Michigan, Ann Arbor
  • Eindhoven University of Technology

Abstract

Understanding the boundary of the set of matrices of nonnegative rank at most r is important for applications in nonconvex optimization. The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component. In fact, this generating set is a Gröbner basis with respect to the graded reverse lexicographic order. This solves a conjecture by Robeva, Sturmfels and the last author.

    Research areas

  • Equivariant Gröbner basis, Mixture model, Nonnegative rank, Stabilization

ID: 6736900