Minimizer extraction in polynomial optimization is robust

Igor Klep, Janez Povh, Jurij Volčič

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this article we present a robustness analysis of the extraction of optimizers in polynomial optimization. Optimizers can be extracted by solving moment problems using flatness and the Gelfand–Naimark–Segal (GNS) construction. Here a modification of the GNS construction is presented that applies even to nonflat data, and then its sensitivity under perturbations is studied. The focus is on eigenvalue optimization for noncommutative polynomials, but we also explain how the main results pertain to commutative and tracial optimization.

Original languageEnglish
Pages (from-to)3177-3207
Number of pages31
JournalSIAM Journal on Optimization
Issue number4
StatePublished - 1 Jan 2018


  • Flat extension
  • GNS construction
  • Hankel matrix
  • Moment problem
  • Noncommutative polynomial
  • Polynomial optimization
  • Semidefinite programming
  • Sum of squares
  • Trace

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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