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Minimizer extraction in polynomial optimization is robust

Igor Klep (igor.klep***at***auckland.ac.nz)
Janez Povh (janez.povh***at***fs.uni-lj.si)
Jurij Volčič (jurij.volcic***at***auckland.ac.nz)

Abstract: 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 non-flat data, and then its sensitivity under perturbations is studied. The focus is on eigenvalue optimization for noncommutative polynomials, but it is also explained how the main results pertain to commutative and tracial optimization.

Keywords: polynomial optimization, sum of squares, semidefinite programming, moment problem, Hankel matrix, flat extension, GNS construction, noncommutative polynomial, trace

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: October 2017

Download: [PDF]

Entry Submitted: 10/06/2017
Entry Accepted: 10/06/2017
Entry Last Modified: 05/29/2018

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