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Polynomial Optimization, Efficiency through Moments and Algebra

Risultati finali

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

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

Pubblicazioni

Construction of multivariate polynomial approximation kernels via semidefinite programming

Autori: Felix Kirschner, Etienne de Klerk
Pubblicato in: 2022
Editore: Arxiv
DOI: 10.48550/arxiv.2203.05892

Exact Moment Representation in Polynomial Optimization

Autori: Baldi, Lorenzo; Mourrain, Bernard
Pubblicato in: 2020, Issue 7, 2020
Editore: N/A

On the degree of varieties of sum of squares

Autori: Ferguson, Andrew; Ottaviani, Giorgio; Safey El Din, Mohab; Turatti, Ettore
Pubblicato in: Issue 55, 2022
Editore: Hal Archive
DOI: 10.48550/arxiv.2206.07473

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

Autori: Schlosser, Corbinian; Korda, Milan
Pubblicato in: 2020, Issue 9, 2020
Editore: N/A

Minimum cross-entropy distributions on Wasserstein balls and their applications

Autori: Vargas, Luis Felipe; Velasco, Mauricio
Pubblicato in: 2021
Editore: Arxiv
DOI: 10.48550/arxiv.2106.03226

Converging approximations of attractors via almost Lyapunov functions and semidefinite programming

Autori: Corbinian Schlosser
Pubblicato in: 2022
Editore: Arxiv
DOI: 10.48550/arxiv.2203.02806

Degree bounds for Putinar's Positivstellensatz on the hypercube

Autori: Baldi, Lorenzo; Slot, Lucas
Pubblicato in: 2023
Editore: Arxiv
DOI: 10.48550/arxiv.2302.12558

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

Autori: Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Pubblicato in: 2023
Editore: Hal Archive

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

Autori: Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Pubblicato in: 2023
Editore: Hal Archive

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

Autori: Habibi, Soodeh; Kavand, Arefeh; Kocvara, Michal; Stingl, Michael
Pubblicato in: 2021
Editore: Arxiv
DOI: 10.48550/arxiv.2105.08529

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

Autori: Evelyne Hubert, Tobias Metzlaff, Cordian Riener
Pubblicato in: 2022
Editore: Hal Archive
DOI: 10.48550/arxiv.2203.13152

The Wonderful Geometry of the Vandermonde map

Autori: Jose Acevedo, Grigoriy Blekherman, Sebastian Debus, Cordian Riener
Pubblicato in: 2023
Editore: Arxiv
DOI: 10.48550/arxiv.2303.09512

Semidefinite approximations for bicliques and biindependent pairs

Autori: Monique Laurent, Sven Polak, Luis Felipe Vargas
Pubblicato in: 2023
Editore: Arxiv
DOI: 10.48550/arxiv.2302.08886

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

Autori: Hubert, Evelyne; Metzlaff, Tobias; Moustrou, Philippe; Riener, Cordian
Pubblicato in: Issue 33, 2023
Editore: Arxiv
DOI: 10.48550/arxiv.2303.09487

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

Autori: Steenkamp, Andries
Pubblicato in: Journal of Portfolio Management, 2023, Issue 82, 2023
Editore: Arxiv
DOI: 10.48550/arxiv.2302.10573

Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems

Autori: Magron, Victor; Wang, Jie; Schlosser, Corbinian; Korda, Milan
Pubblicato in: Issue 3, 2023
Editore: IEEE Transactions on Automatic Control
DOI: 10.48550/arxiv.2111.08347

Reflection groups and cones of sums of squares

Autori: Debus, Sebastian; Riener, Cordian
Pubblicato in: 2020, Issue 8, 2020
Editore: N/A

Computing real radicals by moment optimization

Autori: Lorenzo Baldi (ESR9, Inria), Bernard Mourrain
Pubblicato in: 2020
Editore: N/A

Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces

Autori: Masahiro Ikeda, Isao Ishikawa,Corbinian Schlosser
Pubblicato in: 2022
Editore: AIP Publishing
DOI: 10.1063/5.0094889

Converging outer approximations to global attractors using semidefinite programming

Autori: Schlosser, Corbinian; Korda, Milan
Pubblicato in: 2020, Issue 3, 2020
Editore: N/A

A second order cone characterization for sums of nonnegative circuits

Autori: Magron, Victor; Wang, Jie
Pubblicato in: 2020, Issue 1, 2020
Editore: Hal

TSSOS: A Moment-SOS hierarchy that exploits term sparsity

Autori: Wang, Jie; Magron, Victor; Lasserre, Jean-Bernard
Pubblicato in: 2020, Issue 1, 2020
Editore: Hal

Computing controlled invariant sets from data using convex optimization

Autori: Korda, Milan
Pubblicato in: https://hal.archives-ouvertes.fr/hal-02398027, Issue 1, 2019
Editore: Hal

Computing the Hausdorff boundary measure of semi-algebraic sets

Autori: Lasserre, Jean-Bernard; Magron, Victor
Pubblicato in: 2020, Issue 1, 2020
Editore: Hal

A sparse version of Reznick's Positivstellensatz

Autori: Mai, N. H. A.; Magron, Victor; Lasserre, Jean-Bernard
Pubblicato in: 2020, Issue 1, 2020
Editore: Hal

Symmetric Ideals, Specht Polynomials and Solutions to Symmetric Systems of Equations

Autori: Philippe Moustrou, Cordian Riener, Hugues Verdure
Pubblicato in: 2019
Editore: Hal

Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial minimization on the sphere

Autori: Etienne de Klerk, Monique Laurent
Pubblicato in: 2019
Editore: Hal

The poset of Specht ideals for hyperoctahedral groups

Autori: Sebastian Debus, Philippe Moustrou, Cordian Riener, Hugues Verdure
Pubblicato in: 2022
Editore: Arxiv
DOI: 10.48550/arxiv.2206.08925

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

Autori: Levandovskyy, Viktor; Metzlaff, Tobias; Zeid, Karim,
Pubblicato in: 2020, Issue 10, 2020
Editore: N/A

Binary forms of suprageneric rank and the multiple root loci

Autori: Nevado, Alejandro González; Turatti, Ettore Teixeira
Pubblicato in: 2020
Editore: Arvix
DOI: 10.48550/arxiv.2007.03335

On Łojasiewicz Inequalities and the Effective Putinar's Positivstellensatz

Autori: Baldi, Lorenzo; Mourrain, Bernard; Parusinski, Adam
Pubblicato in: 2022
Editore: Arxiv
DOI: 10.48550/arxiv.2212.09551

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

Autori: Felix Kirschner, Etienne de Klerk
Pubblicato in: 2023
Editore: Arxiv
DOI: 10.48550/arxiv.2301.06368

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

Autori: Berthomieu, Jérémy; Ferguson, Andrew; Safey El Din, Mohab
Pubblicato in: 2022
Editore: Hal Sorbonne
DOI: 10.48550/arxiv.2104.00913

Polynomial Optimization, Moments, and Applications

Autori: Kočvara, Michal; Mourrain, Bernard; Riener, Cordian
Pubblicato in: Polynomial Optimization, Moments, and Applications, 2023, ISBN 978-3-031-38659-6
Editore: Springers

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

Autori: Korda, Milan; Laurent, Monique; Magron, Victor; Steenkamp, Andries
Pubblicato in: Mathematical Programming, Issue 10, 2023, ISSN 1436-4646
Editore: Springer
DOI: 10.48550/arxiv.2209.09573

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

Autori: Monique Laurent, Luis Felipe Vargas
Pubblicato in: Linear Algebra and its Applications, Issue Volume 651, 2022, ISSN 0024-3795
Editore: Elsevier BV
DOI: 10.1016/j.laa.2022.06.015

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

Autori: Luca Sodomaco, Ettore Teixeira Turatti
Pubblicato in: Journal of Symbolic Computation, 2023, ISSN 0747-7171
Editore: Academic Press
DOI: 10.1016/j.jsc.2023.102230

Decomposition of arrow type positive semidefinite matrices with application to topology optimization

Autori: Michal Kočvara; Michal Kočvara
Pubblicato in: Mathematical Programming, Issue 90, 2021, ISSN 0025-5610
Editore: Springer Verlag
DOI: 10.1007/s10107-020-01526-w

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

Autori: Monique Laurent; Luis Felipe Vargas
Pubblicato in: Mathematics of Operations Research, Issue 83, 2022, ISSN 0364-765X
Editore: Institute for Operations Research and the Management Sciences
DOI: 10.48550/arxiv.2109.12876

Reflection groups and cones of sums of squares

Autori: Sebastian Debus; Cordian Riener
Pubblicato in: Journal of Symbolic Computation, Issue Vol. 119, 2023, ISSN 0747-7171
Editore: Academic Press
DOI: 10.1016/j.jsc.2023.03.001

On the Effective Putinar’s Positivstellensatz and Moment Approximation

Autori: Lorenzo Baldi; Bernard Mourrain
Pubblicato in: Mathematical Programming, 2023, ISSN 1436-4646
Editore: Springers
DOI: 10.1007/s10107-022-01877-6

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

Autori: Brosch, Daniel; Laurent, Monique; Steenkamp, Andries
Pubblicato in: SIAM Journal on Optimization, Issue Vol. 31, Iss. 3 (2021), 2021, ISSN 1095-7189
Editore: SIAM
DOI: 10.1137/20m1369592

Bounding the separable rank via polynomial optimization

Autori: Sander Gribling; Monique Laurent; Andries Steenkamp
Pubblicato in: Linear Algebra and its Applications, Issue 39, 2022, ISSN 0024-3795
Editore: Elsevier BV
DOI: 10.1016/j.laa.2022.04.010

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

Autori: Monique Laurent; Luis Felipe Vargas
Pubblicato in: SIAM Journal on Optimization, Issue Volume 32, Issue 2, June 2022, 2022, ISSN 1095-7189
Editore: SIAM
DOI: 10.48550/arxiv.2103.01574

Polynomial description for the T-Orbit Spaces of Multiplicative Actions

Autori: Hubert, Evelyne; Metzlaff, Tobias; Riener, Cordian
Pubblicato in: ACM Communications in Computer Algebra, Issue 12, 2022, ISSN 1932-2240
Editore: ACM
DOI: 10.1145/3572867.3572879

On tensors that are determined by their singular tuples

Autori: Ettore Teixeira Turatti
Pubblicato in: SIAM Journal on Applied Algebra and Geometry, Issue 68, 2022, ISSN 2470-6566
Editore: SIAM
DOI: 10.1137/21m1412980

On the solution existence and stability of polynomial optimization problems

Autori: Vu, Trung-Hieu
Pubblicato in: Optimization Letters, 2022, ISSN 1862-4480
Editore: Springers
DOI: 10.48550/arxiv.1808.06100

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

Autori: Victor Magron; Mohab Safey El Din; Trung-Hieu Vu
Pubblicato in: SIAM Journal on Optimization, 2023, ISSN 1095-7189
Editore: SIAM
DOI: 10.1137/21m1436245

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

Autori: Didier Henrion; Felix Kirschner; Etienne De Klerk; Milan Korda; Jean-Bernard Lasserre; Victor Magron
Pubblicato in: INFORMS Journal on Computing, Issue Volume 35, Issue 2, 2023, ISSN 1526-5528
Editore: INFORMS Pub Online
DOI: 10.48550/arxiv.2111.07701

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

Autori: Trung-Hieu Vu
Pubblicato in: Set-Valued and Variational Analysis volume, 2022, ISSN 1877-0541
Editore: Springers
DOI: 10.1007/s11228-022-00637-0

Sparsity Structures for Koopman and Perron--Frobenius Operators

Autori: Corbinian Schlosser; Milan Korda
Pubblicato in: SIAM Journal on Applied Dynamical Systems, Issue Volume 21Issue 3pp. 1663-2296, 2021, ISSN 1536-0040
Editore: 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

Autori: Etienne De Klerk; Felix Kirschner
Pubblicato in: Optimization Letters, 2022, ISSN 1862-4480
Editore: Springers
DOI: 10.1007/s11590-022-01851-3

Computing minimal Gorenstein covers

Autori: Juan Elias, Roser Homs, Bernard Mourrain
Pubblicato in: Journal of Pure and Applied Algebra, Issue 224/7, 2020, Page(s) 106280, ISSN 0022-4049
Editore: Elsevier BV
DOI: 10.1016/j.jpaa.2019.106280

Towards fast one-block quantifier elimination through generalised critical values

Autori: Jérémy Berthomieu, Andrew Ferguson, Mohab Safey El Din
Pubblicato in: ACM Communications in Computer Algebra, Issue 54/3, 2020, Page(s) 109-113, ISSN 1932-2240
Editore: ACM Communications in Computer Algebra
DOI: 10.1145/3457341.3457348

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

Autori: Jérémy Berthomieu; Alin Bostan; Andrew Ferguson; Mohab Safey El Din
Pubblicato in: Journal of Algebra Volume 602, Issue 154-180, 2022, ISSN 0021-8693
Editore: Academic Press
DOI: 10.1016/j.jalgebra.2022.03.002

Conic Optimization with Applications in Finance and Approximation Theory

Autori: Felix Kirschner
Pubblicato in: 2023, ISBN 9789056687090
Editore: Tilburg University
DOI: 10.26116/x0f5-4k25

Crystallographic groups and Chebyshev polynomials in global optimization

Autori: Tobias Metzlaff
Pubblicato in: 2022
Editore: Inria

Effective representations in real algebraic geometry and polynomial optimization

Autori: Lorenzo Baldi
Pubblicato in: 2022
Editore: Inria Université Cote d'Azur

Exact Algorithms for Polynomial Optimisation

Autori: Andrew Ferguson
Pubblicato in: 2022
Editore: Sorbonne University

Certified Polynomial Optimization Based on Exact Sum of Squares Decompositions

Autori: Vu Trung Hieu
Pubblicato in: 2022
Editore: Hal

Combinatorics of Reflection Groups and Real Algebraic Geometry

Autori: Debus, Sebastian
Pubblicato in: Issue 2, 2022
Editore: The Arctic University of Norway

Singular vector tuples and their geometry

Autori: Ettore Teixeira Turatti
Pubblicato in: 2022
Editore: University of Florence

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

Autori: Vargas, Luis,; Laurent, Monique
Pubblicato in: POEMA Book - Polynomial Optimization, Moments, and Applications, Issue 69, 2023
Editore: Springer
DOI: 10.48550/arxiv.2302.04690

Polynomial optimization in geometric modeling

Autori: Soodeh Habibi, Michal Kočvara, Bernard Mourrain
Pubblicato in: POEMA Book - Polynomial Optimization, Moments, and Applications, 2023
Editore: Springer

A Survey of Semidefinite Programming Approaches to the Generalized Problem of Moments and Their Error Analysis

Autori: Etienne de Klerk, Monique Laurent
Pubblicato in: World Women in Mathematics 2018 - Proceedings of the First World Meeting for Women in Mathematics (WM)², Issue 20, 2019, Page(s) 17-56, ISBN 978-3-030-21169-1
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-21170-7_1

A Survey of Semidefinite Programming Approaches to the Generalized Problem of Moments and Their Error Analysis

Autori: Etienne de Klerk, Monique Laurent
Pubblicato in: 2019
Editore: World Women in Mathematics 2018, 2019

Matrix factorization ranks via polynomial optimization

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

Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients

Autori: Magron, Victor; Safey El Din, Mohab; Schweighofer, Markus; Vu, Trung Hieu
Pubblicato in: International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2022, Lille, France, Issue 86, 2022, ISBN 9781450386883
Editore: ACM
DOI: 10.48550/arxiv.2202.06544

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

Autori: Viktor Levandovskyy, Tobias Metzlaff, Karim Abou Zeid
Pubblicato in: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020, Page(s) 312-319, ISBN 9781450371001
Editore: ACM
DOI: 10.1145/3373207.3404052

Polynomial optimization based schemes for solving AC Optimal Power Flow problems

Autori: Fuentes, Edgar; Mourrain, Bernard; Gabay, Michaël
Pubblicato in: https://www.euro-online.org/, 2023
Editore: Euro Online

Computing the volume of compact semi-algebraic sets

Autori: Lairez, Pierre; Mezzarobba, Marc; Safey El Din, Mohab
Pubblicato in: ISSAC 2019, 2019
Editore: ISAAC

Computing minimal Gorenstein covers

Autori: Juan Elias, Roser Homs, Bernard Mourrain
Pubblicato in: Journal of Pure and Applied Algebra, 2019
Editore: Elsevier

Computing real radicals and S-radicals of polynomial systems

Autori: Mohab Safey El Din, Zhi-Hong Yang, Lihong Zhi
Pubblicato in: Journal of Symbolic Computation, 2019
Editore: Elsevier

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

Autori: Ferguson, Andrew; Le, Huu Phuoc
Pubblicato in: ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Issue 9, 2022
Editore: ACM
DOI: 10.1145/3476446.3536182

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