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.
Original language | English |
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Pages (from-to) | 3177-3207 |
Number of pages | 31 |
Journal | SIAM Journal on Optimization |
Volume | 28 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jan 2018 |
Keywords
- 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