Polynomial Optimization, Efficiency through Moments and Algebra

Información del proyecto

POEMA

Identificador del acuerdo de subvención: 813211

DOI

10.3030/813211

Proyecto cerrado

Fecha de la firma de la CE 30 Agosto 2018

Fecha de inicio 1 Enero 2019

Fecha de finalización 30 Junio 2023

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 4 015 251,30

Aportación de la UE

€ 4 015 251,30

Coordinado por

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE
France

CORDIS proporciona enlaces a los documentos públicos y las publicaciones de los proyectos de los programas marco HORIZONTE.

Los enlaces a los documentos y las publicaciones de los proyectos del Séptimo Programa Marco, así como los enlaces a algunos tipos de resultados específicos, como conjuntos de datos y «software», se obtienen dinámicamente de OpenAIRE .

Resultado final

Documents, reports (5)

Research progress on applications of polynomial optimization

Report on Research progress on applications of polynomial optimization

Research progress on algebraic techniques for polynomial optimization

Report on the Research progress on algebraic techniques for polynomial optimization

Research progress on exploiting structures in polynomial optimization

Report on Research progress on exploiting structures in polynomial optimization

Research progress on mixed-integer nonlinear programming

Report on Research progress on mixed-integer nonlinear programming

First report on training

Report on the events and the training programme for the first period

Websites, patent fillings, videos etc. (3)

Report on network activities and the content and use of the web site for on-line courses, publications, test suite and software presentations

Progress report on network activities including content and use of the web site

Web site for on-line courses, publications, test suite and software presentations

Portal for online courses, presentations. seminars, test suite and software presentations

Network web site

Web server for the internal and external communication

Publicaciones

Other (23)

Construction of multivariate polynomial approximation kernels via semidefinite programming

Autores: Felix Kirschner, Etienne de Klerk
Publicado en: 2022
Editor: Arxiv
DOI: 10.48550/arxiv.2203.05892

Exact Moment Representation in Polynomial Optimization

Autores: Baldi, Lorenzo; Mourrain, Bernard
Publicado en: SSRN, 2020
Editor: SSRN
DOI: 10.2139/ssrn.4453226

On the degree of varieties of sum of squares

Autores: Ferguson, Andrew; Ottaviani, Giorgio; Safey El Din, Mohab; Turatti, Ettore
Publicado en: Edición 55, 2022
Editor: Hal Archive
DOI: 10.48550/arxiv.2206.07473

Minimum cross-entropy distributions on Wasserstein balls and their applications

Autores: Vargas, Luis Felipe; Velasco, Mauricio
Publicado en: 2021
Editor: Arxiv
DOI: 10.48550/arxiv.2106.03226

Converging approximations of attractors via almost Lyapunov functions and semidefinite programming

Autores: Corbinian Schlosser
Publicado en: 2022
Editor: Arxiv
DOI: 10.48550/arxiv.2203.02806

Degree bounds for Putinar's Positivstellensatz on the hypercube

Autores: Baldi, Lorenzo; Slot, Lucas
Publicado en: 2023
Editor: Arxiv
DOI: 10.48550/arxiv.2302.12558

Loraine - An interior-point solver for low-rank semidefinite programming

Autores: Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Publicado en: 2023
Editor: Hal Archive

Solving Lasserre relaxations of unconstrained binary quadratic optimization problems by an interior-point method

Autores: Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Publicado en: 2023
Editor: Hal Archive

Barrier and penalty methods for low-rank semidefinite programming with application to truss topology design

Autores: Habibi, Soodeh; Kavand, Arefeh; Kocvara, Michal; Stingl, Michael
Publicado en: 2021
Editor: Arxiv
DOI: 10.48550/arxiv.2105.08529

Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description

Autores: Evelyne Hubert, Tobias Metzlaff, Cordian Riener
Publicado en: 2022
Editor: Hal Archive
DOI: 10.48550/arxiv.2203.13152

The Wonderful Geometry of the Vandermonde map

Autores: Jose Acevedo, Grigoriy Blekherman, Sebastian Debus, Cordian Riener
Publicado en: 2023
Editor: Arxiv
DOI: 10.48550/arxiv.2303.09512

Semidefinite approximations for bicliques and biindependent pairs

Autores: Monique Laurent, Sven Polak, Luis Felipe Vargas
Publicado en: 2023
Editor: Arxiv
DOI: 10.48550/arxiv.2302.08886

Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs

Autores: Hubert, Evelyne; Metzlaff, Tobias; Moustrou, Philippe; Riener, Cordian
Publicado en: Edición 33, 2023
Editor: Arxiv
DOI: 10.48550/arxiv.2303.09487

Convex scalarizations of the mean-variance-skewness-kurtosis problem in portfolio selection

Autores: Steenkamp, Andries
Publicado en: Journal of Portfolio Management, 2023, Edición 82, 2023
Editor: Arxiv
DOI: 10.48550/arxiv.2302.10573

Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems

Autores: Magron, Victor; Wang, Jie; Schlosser, Corbinian; Korda, Milan
Publicado en: Edición 3, 2023
Editor: IEEE Transactions on Automatic Control
DOI: 10.48550/arxiv.2111.08347

Computing real radicals by moment optimization

Autores: Lorenzo Baldi (ESR9, Inria), Bernard Mourrain
Publicado en: 2020
Editor: N/A

Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces

Autores: Masahiro Ikeda, Isao Ishikawa,Corbinian Schlosser
Publicado en: 2022
Editor: AIP Publishing
DOI: 10.1063/5.0094889

Converging outer approximations to global attractors using semidefinite programming

Autores: Schlosser, Corbinian; Korda, Milan
Publicado en: No journal title, 2020
Editor: Arxiv
DOI: 10.48550/arxiv.2005.03346

The poset of Specht ideals for hyperoctahedral groups

Autores: Sebastian Debus, Philippe Moustrou, Cordian Riener, Hugues Verdure
Publicado en: 2022
Editor: Arxiv
DOI: 10.48550/arxiv.2206.08925

Binary forms of suprageneric rank and the multiple root loci

Autores: Nevado, Alejandro González; Turatti, Ettore Teixeira
Publicado en: 2020
Editor: Arvix
DOI: 10.48550/arxiv.2007.03335

On Łojasiewicz Inequalities and the Effective Putinar's Positivstellensatz

Autores: Baldi, Lorenzo; Mourrain, Bernard; Parusinski, Adam
Publicado en: 2022
Editor: Arxiv
DOI: 10.48550/arxiv.2212.09551

A predictor-corrector algorithm for semidefinite programming that uses the factor width cone

Autores: Felix Kirschner, Etienne de Klerk
Publicado en: 2023
Editor: Arxiv
DOI: 10.48550/arxiv.2301.06368

Computing the set of asymptotic critical values of polynomial mappings from smooth algebraic sets

Autores: Berthomieu, Jérémy; Ferguson, Andrew; Safey El Din, Mohab
Publicado en: 2022
Editor: Hal Sorbonne
DOI: 10.48550/arxiv.2104.00913

Monographic books (1)

Polynomial Optimization, Moments, and Applications

Autores: Kočvara, Michal; Mourrain, Bernard; Riener, Cordian
Publicado en: Polynomial Optimization, Moments, and Applications, 2023, ISBN 978-3-031-38659-6
Editor: Springers

Peer reviewed articles (9)

Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks

Autores: Korda, Milan; Laurent, Monique; Magron, Victor; Steenkamp, Andries
Publicado en: Mathematical Programming, Edición 10, 2023, ISSN 1436-4646
Editor: Springer
DOI: 10.48550/arxiv.2209.09573

On the exactness of sum-of-squares approximations for the cone of 5 × 5 copositive matrices

Autores: Monique Laurent, Luis Felipe Vargas
Publicado en: Linear Algebra and its Applications, Edición Volume 651, 2022, ISSN 0024-3795
Editor: Elsevier BV
DOI: 10.1016/j.laa.2022.06.015

The span of singular tuples of a tensor beyond the boundary format

Autores: Luca Sodomaco, Ettore Teixeira Turatti
Publicado en: Journal of Symbolic Computation, 2023, ISSN 0747-7171
Editor: Academic Press
DOI: 10.1016/j.jsc.2023.102230

Exactness of Parrilo's conic approximations for copositive matrices and associated low order bounds for the stability number of a graph

Autores: Monique Laurent; Luis Felipe Vargas
Publicado en: Mathematics of Operations Research, Edición 83, 2022, ISSN 0364-765X
Editor: Institute for Operations Research and the Management Sciences
DOI: 10.48550/arxiv.2109.12876

Reflection groups and cones of sums of squares

Autores: Sebastian Debus; Cordian Riener
Publicado en: Journal of Symbolic Computation, Edición Vol. 119, 2023, ISSN 0747-7171
Editor: Academic Press
DOI: 10.1016/j.jsc.2023.03.001

On the Effective Putinar’s Positivstellensatz and Moment Approximation

Autores: Lorenzo Baldi; Bernard Mourrain
Publicado en: Mathematical Programming, 2023, ISSN 1436-4646
Editor: Springers
DOI: 10.1007/s10107-022-01877-6

Optimizing hypergraph-based polynomials modeling job-occupancy in queueing with redundancy scheduling

Autores: Brosch, Daniel; Laurent, Monique; Steenkamp, Andries
Publicado en: SIAM Journal on Optimization, Edición Vol. 31, Iss. 3 (2021), 2021, ISSN 1095-7189
Editor: SIAM
DOI: 10.1137/20m1369592

Bounding the separable rank via polynomial optimization

Autores: Sander Gribling; Monique Laurent; Andries Steenkamp
Publicado en: Linear Algebra and its Applications, Edición 39, 2022, ISSN 0024-3795
Editor: Elsevier BV
DOI: 10.1016/j.laa.2022.04.010

Finite convergence of sum-of-squares hierarchies for the stability number of a graph

Autores: Monique Laurent; Luis Felipe Vargas
Publicado en: SIAM Journal on Optimization, Edición Volume 32, Edición 2, June 2022, 2022, ISSN 1095-7189
Editor: SIAM
DOI: 10.48550/arxiv.2103.01574

Conference proceedings (4)

Sparse moment-sum-of-squares relaxations for nonlinear dynamical systems with guaranteed convergence

Autores: Schlosser, Corbinian; Korda, Milan
Publicado en: Congrès SMAI 20, Edición 9, 2020
Editor: Arxiv
DOI: 10.48550/arxiv.2012.05572

Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients

Autores: Magron, Victor; Safey El Din, Mohab; Schweighofer, Markus; Vu, Trung Hieu
Publicado en: International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2022, Lille, France, Edición 86, 2022, ISBN 9781450386883
Editor: ACM
DOI: 10.48550/arxiv.2202.06544

Computation of free non-commutative gröbner bases over Z with Singular:Letterplace

Autores: Viktor Levandovskyy, Tobias Metzlaff, Karim Abou Zeid
Publicado en: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020, Página(s) 312-319, ISBN 9781450371001
Editor: ACM
DOI: 10.1145/3373207.3404052

Finer Complexity Estimates for the Change of Ordering of Gröbner Bases for Generic Symmetric Determinantal Ideals

Autores: Ferguson, Andrew; Le, Huu Phuoc
Publicado en: ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Edición 9, 2022
Editor: ACM
DOI: 10.1145/3476446.3536182

Non-peer reviewed articles (11)

Polynomial description for the T-Orbit Spaces of Multiplicative Actions

Autores: Hubert, Evelyne; Metzlaff, Tobias; Riener, Cordian
Publicado en: ACM Communications in Computer Algebra, Edición 12, 2022, ISSN 1932-2240
Editor: ACM
DOI: 10.1145/3572867.3572879

On tensors that are determined by their singular tuples

Autores: Ettore Teixeira Turatti
Publicado en: SIAM Journal on Applied Algebra and Geometry, Edición 68, 2022, ISSN 2470-6566
Editor: SIAM
DOI: 10.1137/21m1412980

On the solution existence and stability of polynomial optimization problems

Autores: Vu, Trung-Hieu
Publicado en: Optimization Letters, 2022, ISSN 1862-4480
Editor: Springers
DOI: 10.48550/arxiv.1808.06100

Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients

Autores: Victor Magron; Mohab Safey El Din; Trung-Hieu Vu
Publicado en: SIAM Journal on Optimization, 2023, ISSN 1095-7189
Editor: SIAM
DOI: 10.1137/21m1436245

Revisiting semidefinite programming approaches to options pricing: Complexity and computational perspectives

Autores: Didier Henrion; Felix Kirschner; Etienne De Klerk; Milan Korda; Jean-Bernard Lasserre; Victor Magron
Publicado en: INFORMS Journal on Computing, Edición Volume 35, Edición 2, 2023, ISSN 1526-5528
Editor: INFORMS Pub Online
DOI: 10.48550/arxiv.2111.07701

On the Nonemptiness and Boundedness of Solution Sets of Weakly Homogeneous Optimization Problems

Autores: Trung-Hieu Vu
Publicado en: Set-Valued and Variational Analysis volume, 2022, ISSN 1877-0541
Editor: Springers
DOI: 10.1007/s11228-022-00637-0

Sparsity Structures for Koopman and Perron--Frobenius Operators

Autores: Corbinian Schlosser; Milan Korda
Publicado en: SIAM Journal on Applied Dynamical Systems, Edición Volume 21Edición 3pp. 1663-2296, 2021, ISSN 1536-0040
Editor: Society of Industrial and Applied Mathematics
DOI: 10.1137/21m1466608

CONVERGENCE RATES OF RLT AND LASSERRE-TYPE HIERARCHIES FOR THE GENERALIZED MOMENT PROBLEM OVER THE SIMPLEX AND THE SPHERE

Autores: Etienne De Klerk; Felix Kirschner
Publicado en: Optimization Letters, 2022, ISSN 1862-4480
Editor: Springers
DOI: 10.1007/s11590-022-01851-3

Towards fast one-block quantifier elimination through generalised critical values

Autores: Jérémy Berthomieu, Andrew Ferguson, Mohab Safey El Din
Publicado en: ACM Communications in Computer Algebra, Edición 54/3, 2020, Página(s) 109-113, ISSN 1932-2240
Editor: ACM Communications in Computer Algebra
DOI: 10.1145/3457341.3457348

Computing Free Non-commutative Groebner Bases over Z with Singular:Letterplace

Autores: Levandovskyy, Viktor; Metzlaff, Tobias; Zeid, Karim,
Publicado en: Journal of Symbolic Computation, Edición Volume 115, March–April 2023, 2020, Página(s) Pages 201-222, ISSN 0747-7171
Editor: Academic Press
DOI: 10.1016/j.jsc.2022.08.007

"Gr\""obner bases and critical values: The asymptotic combinatorics of determinantal systems"

Autores: Jérémy Berthomieu; Alin Bostan; Andrew Ferguson; Mohab Safey El Din
Publicado en: Journal of Algebra Volume 602, Edición 154-180, 2022, ISSN 0021-8693
Editor: Academic Press
DOI: 10.1016/j.jalgebra.2022.03.002

Thesis and dissertations (7)

Conic Optimization with Applications in Finance and Approximation Theory

Autores: Felix Kirschner
Publicado en: 2023, ISBN 9789056687090
Editor: Tilburg University
DOI: 10.26116/x0f5-4k25

Crystallographic groups and Chebyshev polynomials in global optimization

Autores: Tobias Metzlaff
Publicado en: 2022
Editor: Inria

Effective representations in real algebraic geometry and polynomial optimization

Autores: Lorenzo Baldi
Publicado en: 2022
Editor: Inria Université Cote d'Azur

Exact Algorithms for Polynomial Optimisation

Autores: Andrew Ferguson
Publicado en: 2022
Editor: Sorbonne University

Certified Polynomial Optimization Based on Exact Sum of Squares Decompositions

Autores: Vu Trung Hieu
Publicado en: 2022
Editor: Hal

Combinatorics of Reflection Groups and Real Algebraic Geometry

Autores: Debus, Sebastian
Publicado en: Edición 2, 2022
Editor: The Arctic University of Norway

Singular vector tuples and their geometry

Autores: Ettore Teixeira Turatti
Publicado en: 2022
Editor: University of Florence

Book chapters (3)

Copositive matrices, sums of squares and the stability number of a graph

Autores: Vargas, Luis,; Laurent, Monique
Publicado en: POEMA Book - Polynomial Optimization, Moments, and Applications, Edición 69, 2023
Editor: Springer
DOI: 10.48550/arxiv.2302.04690

Polynomial optimization in geometric modeling

Autores: Soodeh Habibi, Michal Kočvara, Bernard Mourrain
Publicado en: POEMA Book - Polynomial Optimization, Moments, and Applications, 2023
Editor: Springer

Matrix factorization ranks via polynomial optimization

Autores: Steenkamp, Andries
Publicado en: "Michal Kočvara; Bernard Mourrain; Cordian Riener. Polynomial Optimization, Moments, and Applications, Springer, pp.135-162, 2023, ⟨10.48550/arXiv.2302.09994⟩", Edición 21, 2023, ISBN 978-3-031-38659-6
Editor: Arxiv
DOI: 10.48550/arxiv.2302.09994