HARMONIC HIERARCHIES FOR POLYNOMIAL OPTIMIZATION

Sergio Cristancho; Mauricio Velasco

doi:10.1137/22M1484511

HARMONIC HIERARCHIES FOR POLYNOMIAL OPTIMIZATION

Sergio Cristancho, Mauricio Velasco

Universidad de los Andes

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in \BbbRⁿ and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such hierarchies. We also introduce a novel optimization-free algorithm for building converging sequences of lower bounds for polynomial minimization problems on spheres. Finally, some computational results are discussed, showcasing our implementation of these hierarchies in the programming language Julia.

Original language	English
Pages (from-to)	590-615
Number of pages	26
Journal	SIAM Journal on Optimization
Volume	34
Issue number	1
DOIs	https://doi.org/10.1137/22M1484511
State	Published - 2024
Externally published	Yes

Keywords

linear hierarchies
polynomial kernels
polynomial optimization
semidefinite hierarchies

Access to Document

10.1137/22M1484511

Cite this

@article{432897e7945049edb793df24cde4d7da,

title = "HARMONIC HIERARCHIES FOR POLYNOMIAL OPTIMIZATION",

abstract = "We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in \BbbRn and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such hierarchies. We also introduce a novel optimization-free algorithm for building converging sequences of lower bounds for polynomial minimization problems on spheres. Finally, some computational results are discussed, showcasing our implementation of these hierarchies in the programming language Julia.",

keywords = "linear hierarchies, polynomial kernels, polynomial optimization, semidefinite hierarchies",

author = "Sergio Cristancho and Mauricio Velasco",

note = "Publisher Copyright: {\textcopyright} 2024 Society for Industrial and Applied Mathematics.",

year = "2024",

doi = "10.1137/22M1484511",

language = "Ingl{\'e}s",

volume = "34",

pages = "590--615",

journal = "SIAM Journal on Optimization",

issn = "1052-6234",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - HARMONIC HIERARCHIES FOR POLYNOMIAL OPTIMIZATION

AU - Cristancho, Sergio

AU - Velasco, Mauricio

PY - 2024

Y1 - 2024

N2 - We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in \BbbRn and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such hierarchies. We also introduce a novel optimization-free algorithm for building converging sequences of lower bounds for polynomial minimization problems on spheres. Finally, some computational results are discussed, showcasing our implementation of these hierarchies in the programming language Julia.

AB - We introduce novel polyhedral approximation hierarchies for the cone of nonnegative forms on the unit sphere in \BbbRn and for its (dual) cone of moments. We prove computable quantitative bounds on the speed of convergence of such hierarchies. We also introduce a novel optimization-free algorithm for building converging sequences of lower bounds for polynomial minimization problems on spheres. Finally, some computational results are discussed, showcasing our implementation of these hierarchies in the programming language Julia.

KW - linear hierarchies

KW - polynomial kernels

KW - polynomial optimization

KW - semidefinite hierarchies

UR - http://www.scopus.com/inward/record.url?scp=85195238963&partnerID=8YFLogxK

U2 - 10.1137/22M1484511

DO - 10.1137/22M1484511

M3 - Artículo

AN - SCOPUS:85195238963

SN - 1052-6234

VL - 34

SP - 590

EP - 615

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

IS - 1

ER -

HARMONIC HIERARCHIES FOR POLYNOMIAL OPTIMIZATION

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this