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Preprint
Upper bound hierarchies for noncommutative polynomial optimization
arXiv.org
03 Feb 2024
Abstract
This work focuses on minimizing the eigenvalue of a noncommutative polynomial
subject to a finite number of noncommutative polynomial inequality constraints.
Based on the Helton-McCullough Positivstellensatz, the noncommutative analog
of Lasserre's moment-sum of squares hierarchy provides a sequence of lower
bounds converging to the minimal eigenvalue, under mild assumptions on the
constraint set. Each lower bound can be obtained by solving a semidefinite
program.
We derive complementary converging hierarchies of upper bounds. They are
noncommutative analogues of the upper bound hierarchies due to Lasserre for
minimizing polynomials over compact sets. Each upper bound can be obtained by
solving a generalized eigenvalue problem.
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Details
- Title
- Upper bound hierarchies for noncommutative polynomial optimization
- Creators
- Igor KlepVictor Magron - Institut de Mathématiques de ToulouseGaël MasséJurij Volčič - Drexel University
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021861674004721