Igor Klep (Author), Janez Povh (Author), Jurij Volčič (Author)

Abstract

V članku podamo robustnostno analizo ekstrakcije optimizatorjev v polinomski optimizaciji.

Keywords

polinomska optimizacija;vsote kvadratov;semidefinitno programiranje;problem momentov;Hankelova matrika;ploščata razširitev;GNS konstrukcija;nekomutativni polinomi;sled;polynomial optimization;sum of squares;semidefinite programming;moment problem;Hankel matrix;flat extension;GNS construction;noncommutative polynomial;trace;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FS - Faculty of Mechanical Engineering
UDC: 519.85(045)
COBISS: 16398875 Link will open in a new window
ISSN: 1052-6234
Views: 657
Downloads: 644
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Other data

Secondary language: Slovenian
Secondary 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 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.
Secondary keywords: polinomska optimizacija;vsote kvadratov;semidefinitno programiranje;problem momentov;Hankelova matrika;ploščata razširitev;GNS konstrukcija;nekomutativni polinomi;sled;
Type (COBISS): Article
Pages: str. 3177-3207
Volume: ǂVol. ǂ28
Issue: ǂno. ǂ4
Chronology: 2018
DOI: 10.1137/17M1152061
ID: 10993927