Polynomial Optimization, Efficiency through Moments and Algebra

Rezultaty

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

Publikacje

Construction of multivariate polynomial approximation kernels via semidefinite programming

Autorzy: Felix Kirschner, Etienne de Klerk
Opublikowane w: 2022
Wydawca: Arxiv
DOI: 10.48550/arxiv.2203.05892

Exact Moment Representation in Polynomial Optimization

Autorzy: Baldi, Lorenzo; Mourrain, Bernard
Opublikowane w: 2020, Numer 7, 2020
Wydawca: N/A

On the degree of varieties of sum of squares

Autorzy: Ferguson, Andrew; Ottaviani, Giorgio; Safey El Din, Mohab; Turatti, Ettore
Opublikowane w: Numer 55, 2022
Wydawca: Hal Archive
DOI: 10.48550/arxiv.2206.07473

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

Autorzy: Schlosser, Corbinian; Korda, Milan
Opublikowane w: 2020, Numer 9, 2020
Wydawca: N/A

Minimum cross-entropy distributions on Wasserstein balls and their applications

Autorzy: Vargas, Luis Felipe; Velasco, Mauricio
Opublikowane w: 2021
Wydawca: Arxiv
DOI: 10.48550/arxiv.2106.03226

Converging approximations of attractors via almost Lyapunov functions and semidefinite programming

Autorzy: Corbinian Schlosser
Opublikowane w: 2022
Wydawca: Arxiv
DOI: 10.48550/arxiv.2203.02806

Degree bounds for Putinar's Positivstellensatz on the hypercube

Autorzy: Baldi, Lorenzo; Slot, Lucas
Opublikowane w: 2023
Wydawca: Arxiv
DOI: 10.48550/arxiv.2302.12558

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

Autorzy: Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Opublikowane w: 2023
Wydawca: Hal Archive

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

Autorzy: Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Opublikowane w: 2023
Wydawca: Hal Archive

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

Autorzy: Habibi, Soodeh; Kavand, Arefeh; Kocvara, Michal; Stingl, Michael
Opublikowane w: 2021
Wydawca: Arxiv
DOI: 10.48550/arxiv.2105.08529

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

Autorzy: Evelyne Hubert, Tobias Metzlaff, Cordian Riener
Opublikowane w: 2022
Wydawca: Hal Archive
DOI: 10.48550/arxiv.2203.13152

The Wonderful Geometry of the Vandermonde map

Autorzy: Jose Acevedo, Grigoriy Blekherman, Sebastian Debus, Cordian Riener
Opublikowane w: 2023
Wydawca: Arxiv
DOI: 10.48550/arxiv.2303.09512

Semidefinite approximations for bicliques and biindependent pairs

Autorzy: Monique Laurent, Sven Polak, Luis Felipe Vargas
Opublikowane w: 2023
Wydawca: Arxiv
DOI: 10.48550/arxiv.2302.08886

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

Autorzy: Hubert, Evelyne; Metzlaff, Tobias; Moustrou, Philippe; Riener, Cordian
Opublikowane w: Numer 33, 2023
Wydawca: Arxiv
DOI: 10.48550/arxiv.2303.09487

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

Autorzy: Steenkamp, Andries
Opublikowane w: Journal of Portfolio Management, 2023, Numer 82, 2023
Wydawca: Arxiv
DOI: 10.48550/arxiv.2302.10573

Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems

Autorzy: Magron, Victor; Wang, Jie; Schlosser, Corbinian; Korda, Milan
Opublikowane w: Numer 3, 2023
Wydawca: IEEE Transactions on Automatic Control
DOI: 10.48550/arxiv.2111.08347

Computing real radicals by moment optimization

Autorzy: Lorenzo Baldi (ESR9, Inria), Bernard Mourrain
Opublikowane w: 2020
Wydawca: N/A

Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces

Autorzy: Masahiro Ikeda, Isao Ishikawa,Corbinian Schlosser
Opublikowane w: 2022
Wydawca: AIP Publishing
DOI: 10.1063/5.0094889

Converging outer approximations to global attractors using semidefinite programming

Autorzy: Schlosser, Corbinian; Korda, Milan
Opublikowane w: 2020, Numer 3, 2020
Wydawca: N/A

The poset of Specht ideals for hyperoctahedral groups

Autorzy: Sebastian Debus, Philippe Moustrou, Cordian Riener, Hugues Verdure
Opublikowane w: 2022
Wydawca: Arxiv
DOI: 10.48550/arxiv.2206.08925

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

Autorzy: Levandovskyy, Viktor; Metzlaff, Tobias; Zeid, Karim,
Opublikowane w: 2020, Numer 10, 2020
Wydawca: N/A

Binary forms of suprageneric rank and the multiple root loci

Autorzy: Nevado, Alejandro González; Turatti, Ettore Teixeira
Opublikowane w: 2020
Wydawca: Arvix
DOI: 10.48550/arxiv.2007.03335

On Łojasiewicz Inequalities and the Effective Putinar's Positivstellensatz

Autorzy: Baldi, Lorenzo; Mourrain, Bernard; Parusinski, Adam
Opublikowane w: 2022
Wydawca: Arxiv
DOI: 10.48550/arxiv.2212.09551

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

Autorzy: Felix Kirschner, Etienne de Klerk
Opublikowane w: 2023
Wydawca: Arxiv
DOI: 10.48550/arxiv.2301.06368

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

Autorzy: Berthomieu, Jérémy; Ferguson, Andrew; Safey El Din, Mohab
Opublikowane w: 2022
Wydawca: Hal Sorbonne
DOI: 10.48550/arxiv.2104.00913

Polynomial Optimization, Moments, and Applications

Autorzy: Kočvara, Michal; Mourrain, Bernard; Riener, Cordian
Opublikowane w: Polynomial Optimization, Moments, and Applications, 2023, ISBN 978-3-031-38659-6
Wydawca: Springers

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

Autorzy: Korda, Milan; Laurent, Monique; Magron, Victor; Steenkamp, Andries
Opublikowane w: Mathematical Programming, Numer 10, 2023, ISSN 1436-4646
Wydawca: Springer
DOI: 10.48550/arxiv.2209.09573

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

Autorzy: Monique Laurent, Luis Felipe Vargas
Opublikowane w: Linear Algebra and its Applications, Numer Volume 651, 2022, ISSN 0024-3795
Wydawca: Elsevier BV
DOI: 10.1016/j.laa.2022.06.015

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

Autorzy: Luca Sodomaco, Ettore Teixeira Turatti
Opublikowane w: Journal of Symbolic Computation, 2023, ISSN 0747-7171
Wydawca: 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

Autorzy: Monique Laurent; Luis Felipe Vargas
Opublikowane w: Mathematics of Operations Research, Numer 83, 2022, ISSN 0364-765X
Wydawca: Institute for Operations Research and the Management Sciences
DOI: 10.48550/arxiv.2109.12876

Reflection groups and cones of sums of squares

Autorzy: Sebastian Debus; Cordian Riener
Opublikowane w: Journal of Symbolic Computation, Numer Vol. 119, 2023, ISSN 0747-7171
Wydawca: Academic Press
DOI: 10.1016/j.jsc.2023.03.001

On the Effective Putinar’s Positivstellensatz and Moment Approximation

Autorzy: Lorenzo Baldi; Bernard Mourrain
Opublikowane w: Mathematical Programming, 2023, ISSN 1436-4646
Wydawca: Springers
DOI: 10.1007/s10107-022-01877-6

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

Autorzy: Brosch, Daniel; Laurent, Monique; Steenkamp, Andries
Opublikowane w: SIAM Journal on Optimization, Numer Vol. 31, Iss. 3 (2021), 2021, ISSN 1095-7189
Wydawca: SIAM
DOI: 10.1137/20m1369592

Bounding the separable rank via polynomial optimization

Autorzy: Sander Gribling; Monique Laurent; Andries Steenkamp
Opublikowane w: Linear Algebra and its Applications, Numer 39, 2022, ISSN 0024-3795
Wydawca: Elsevier BV
DOI: 10.1016/j.laa.2022.04.010

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

Autorzy: Monique Laurent; Luis Felipe Vargas
Opublikowane w: SIAM Journal on Optimization, Numer Volume 32, Numer 2, June 2022, 2022, ISSN 1095-7189
Wydawca: SIAM
DOI: 10.48550/arxiv.2103.01574

Polynomial description for the T-Orbit Spaces of Multiplicative Actions

Autorzy: Hubert, Evelyne; Metzlaff, Tobias; Riener, Cordian
Opublikowane w: ACM Communications in Computer Algebra, Numer 12, 2022, ISSN 1932-2240
Wydawca: ACM
DOI: 10.1145/3572867.3572879

On tensors that are determined by their singular tuples

Autorzy: Ettore Teixeira Turatti
Opublikowane w: SIAM Journal on Applied Algebra and Geometry, Numer 68, 2022, ISSN 2470-6566
Wydawca: SIAM
DOI: 10.1137/21m1412980

On the solution existence and stability of polynomial optimization problems

Autorzy: Vu, Trung-Hieu
Opublikowane w: Optimization Letters, 2022, ISSN 1862-4480
Wydawca: Springers
DOI: 10.48550/arxiv.1808.06100

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

Autorzy: Victor Magron; Mohab Safey El Din; Trung-Hieu Vu
Opublikowane w: SIAM Journal on Optimization, 2023, ISSN 1095-7189
Wydawca: SIAM
DOI: 10.1137/21m1436245

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

Autorzy: Didier Henrion; Felix Kirschner; Etienne De Klerk; Milan Korda; Jean-Bernard Lasserre; Victor Magron
Opublikowane w: INFORMS Journal on Computing, Numer Volume 35, Numer 2, 2023, ISSN 1526-5528
Wydawca: INFORMS Pub Online
DOI: 10.48550/arxiv.2111.07701

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

Autorzy: Trung-Hieu Vu
Opublikowane w: Set-Valued and Variational Analysis volume, 2022, ISSN 1877-0541
Wydawca: Springers
DOI: 10.1007/s11228-022-00637-0

Sparsity Structures for Koopman and Perron--Frobenius Operators

Autorzy: Corbinian Schlosser; Milan Korda
Opublikowane w: SIAM Journal on Applied Dynamical Systems, Numer Volume 21Numer 3pp. 1663-2296, 2021, ISSN 1536-0040
Wydawca: 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

Autorzy: Etienne De Klerk; Felix Kirschner
Opublikowane w: Optimization Letters, 2022, ISSN 1862-4480
Wydawca: Springers
DOI: 10.1007/s11590-022-01851-3

Towards fast one-block quantifier elimination through generalised critical values

Autorzy: Jérémy Berthomieu, Andrew Ferguson, Mohab Safey El Din
Opublikowane w: ACM Communications in Computer Algebra, Numer 54/3, 2020, Strona(/y) 109-113, ISSN 1932-2240
Wydawca: ACM Communications in Computer Algebra
DOI: 10.1145/3457341.3457348

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

Autorzy: Jérémy Berthomieu; Alin Bostan; Andrew Ferguson; Mohab Safey El Din
Opublikowane w: Journal of Algebra Volume 602, Numer 154-180, 2022, ISSN 0021-8693
Wydawca: Academic Press
DOI: 10.1016/j.jalgebra.2022.03.002

Conic Optimization with Applications in Finance and Approximation Theory

Autorzy: Felix Kirschner
Opublikowane w: 2023, ISBN 9789056687090
Wydawca: Tilburg University
DOI: 10.26116/x0f5-4k25

Crystallographic groups and Chebyshev polynomials in global optimization

Autorzy: Tobias Metzlaff
Opublikowane w: 2022
Wydawca: Inria

Effective representations in real algebraic geometry and polynomial optimization

Autorzy: Lorenzo Baldi
Opublikowane w: 2022
Wydawca: Inria Université Cote d'Azur

Exact Algorithms for Polynomial Optimisation

Autorzy: Andrew Ferguson
Opublikowane w: 2022
Wydawca: Sorbonne University

Certified Polynomial Optimization Based on Exact Sum of Squares Decompositions

Autorzy: Vu Trung Hieu
Opublikowane w: 2022
Wydawca: Hal

Combinatorics of Reflection Groups and Real Algebraic Geometry

Autorzy: Debus, Sebastian
Opublikowane w: Numer 2, 2022
Wydawca: The Arctic University of Norway

Singular vector tuples and their geometry

Autorzy: Ettore Teixeira Turatti
Opublikowane w: 2022
Wydawca: University of Florence

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

Autorzy: Vargas, Luis,; Laurent, Monique
Opublikowane w: POEMA Book - Polynomial Optimization, Moments, and Applications, Numer 69, 2023
Wydawca: Springer
DOI: 10.48550/arxiv.2302.04690

Polynomial optimization in geometric modeling

Autorzy: Soodeh Habibi, Michal Kočvara, Bernard Mourrain
Opublikowane w: POEMA Book - Polynomial Optimization, Moments, and Applications, 2023
Wydawca: Springer

Matrix factorization ranks via polynomial optimization

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

Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients

Autorzy: Magron, Victor; Safey El Din, Mohab; Schweighofer, Markus; Vu, Trung Hieu
Opublikowane w: International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2022, Lille, France, Numer 86, 2022, ISBN 9781450386883
Wydawca: ACM
DOI: 10.48550/arxiv.2202.06544

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

Autorzy: Viktor Levandovskyy, Tobias Metzlaff, Karim Abou Zeid
Opublikowane w: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020, Strona(/y) 312-319, ISBN 9781450371001
Wydawca: ACM
DOI: 10.1145/3373207.3404052

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

Autorzy: Ferguson, Andrew; Le, Huu Phuoc
Opublikowane w: ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Numer 9, 2022
Wydawca: ACM
DOI: 10.1145/3476446.3536182

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