Polynomial Optimization, Efficiency through Moments and Algebra

Deliverables

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

Publications

Construction of multivariate polynomial approximation kernels via semidefinite programming

Author(s): Felix Kirschner, Etienne de Klerk
Published in: 2022
Publisher: Arxiv
DOI: 10.48550/arxiv.2203.05892

Exact Moment Representation in Polynomial Optimization

Author(s): Baldi, Lorenzo; Mourrain, Bernard
Published in: 2020, Issue 7, 2020
Publisher: N/A

On the degree of varieties of sum of squares

Author(s): Ferguson, Andrew; Ottaviani, Giorgio; Safey El Din, Mohab; Turatti, Ettore
Published in: Issue 55, 2022
Publisher: Hal Archive
DOI: 10.48550/arxiv.2206.07473

Minimum cross-entropy distributions on Wasserstein balls and their applications

Author(s): Vargas, Luis Felipe; Velasco, Mauricio
Published in: 2021
Publisher: Arxiv
DOI: 10.48550/arxiv.2106.03226

Converging approximations of attractors via almost Lyapunov functions and semidefinite programming

Author(s): Corbinian Schlosser
Published in: 2022
Publisher: Arxiv
DOI: 10.48550/arxiv.2203.02806

Degree bounds for Putinar's Positivstellensatz on the hypercube

Author(s): Baldi, Lorenzo; Slot, Lucas
Published in: 2023
Publisher: Arxiv
DOI: 10.48550/arxiv.2302.12558

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

Author(s): Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Published in: 2023
Publisher: Hal Archive

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

Author(s): Habibi, Soodeh; Kočvara, Michal; Stingl, Michael
Published in: 2023
Publisher: Hal Archive

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

Author(s): Habibi, Soodeh; Kavand, Arefeh; Kocvara, Michal; Stingl, Michael
Published in: 2021
Publisher: Arxiv
DOI: 10.48550/arxiv.2105.08529

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

Author(s): Evelyne Hubert, Tobias Metzlaff, Cordian Riener
Published in: 2022
Publisher: Hal Archive
DOI: 10.48550/arxiv.2203.13152

The Wonderful Geometry of the Vandermonde map

Author(s): Jose Acevedo, Grigoriy Blekherman, Sebastian Debus, Cordian Riener
Published in: 2023
Publisher: Arxiv
DOI: 10.48550/arxiv.2303.09512

Semidefinite approximations for bicliques and biindependent pairs

Author(s): Monique Laurent, Sven Polak, Luis Felipe Vargas
Published in: 2023
Publisher: Arxiv
DOI: 10.48550/arxiv.2302.08886

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

Author(s): Hubert, Evelyne; Metzlaff, Tobias; Moustrou, Philippe; Riener, Cordian
Published in: Issue 33, 2023
Publisher: Arxiv
DOI: 10.48550/arxiv.2303.09487

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

Author(s): Steenkamp, Andries
Published in: Journal of Portfolio Management, 2023, Issue 82, 2023
Publisher: Arxiv
DOI: 10.48550/arxiv.2302.10573

Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems

Author(s): Magron, Victor; Wang, Jie; Schlosser, Corbinian; Korda, Milan
Published in: Issue 3, 2023
Publisher: IEEE Transactions on Automatic Control
DOI: 10.48550/arxiv.2111.08347

Computing real radicals by moment optimization

Author(s): Lorenzo Baldi (ESR9, Inria), Bernard Mourrain
Published in: 2020
Publisher: N/A

Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces

Author(s): Masahiro Ikeda, Isao Ishikawa,Corbinian Schlosser
Published in: 2022
Publisher: AIP Publishing
DOI: 10.1063/5.0094889

Converging outer approximations to global attractors using semidefinite programming

Author(s): Schlosser, Corbinian; Korda, Milan
Published in: 2020, Issue 3, 2020
Publisher: N/A

The poset of Specht ideals for hyperoctahedral groups

Author(s): Sebastian Debus, Philippe Moustrou, Cordian Riener, Hugues Verdure
Published in: 2022
Publisher: Arxiv
DOI: 10.48550/arxiv.2206.08925

Binary forms of suprageneric rank and the multiple root loci

Author(s): Nevado, Alejandro González; Turatti, Ettore Teixeira
Published in: 2020
Publisher: Arvix
DOI: 10.48550/arxiv.2007.03335

On Łojasiewicz Inequalities and the Effective Putinar's Positivstellensatz

Author(s): Baldi, Lorenzo; Mourrain, Bernard; Parusinski, Adam
Published in: 2022
Publisher: Arxiv
DOI: 10.48550/arxiv.2212.09551

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

Author(s): Felix Kirschner, Etienne de Klerk
Published in: 2023
Publisher: Arxiv
DOI: 10.48550/arxiv.2301.06368

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

Author(s): Berthomieu, Jérémy; Ferguson, Andrew; Safey El Din, Mohab
Published in: 2022
Publisher: Hal Sorbonne
DOI: 10.48550/arxiv.2104.00913

Polynomial Optimization, Moments, and Applications

Author(s): Kočvara, Michal; Mourrain, Bernard; Riener, Cordian
Published in: Polynomial Optimization, Moments, and Applications, 2023, ISBN 978-3-031-38659-6
Publisher: Springers

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

Author(s): Korda, Milan; Laurent, Monique; Magron, Victor; Steenkamp, Andries
Published in: Mathematical Programming, Issue 10, 2023, ISSN 1436-4646
Publisher: Springer
DOI: 10.48550/arxiv.2209.09573

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

Author(s): Monique Laurent, Luis Felipe Vargas
Published in: Linear Algebra and its Applications, Issue Volume 651, 2022, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2022.06.015

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

Author(s): Luca Sodomaco, Ettore Teixeira Turatti
Published in: Journal of Symbolic Computation, 2023, ISSN 0747-7171
Publisher: 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

Author(s): Monique Laurent; Luis Felipe Vargas
Published in: Mathematics of Operations Research, Issue 83, 2022, ISSN 0364-765X
Publisher: Institute for Operations Research and the Management Sciences
DOI: 10.48550/arxiv.2109.12876

Reflection groups and cones of sums of squares

Author(s): Sebastian Debus; Cordian Riener
Published in: Journal of Symbolic Computation, Issue Vol. 119, 2023, ISSN 0747-7171
Publisher: Academic Press
DOI: 10.1016/j.jsc.2023.03.001

On the Effective Putinar’s Positivstellensatz and Moment Approximation

Author(s): Lorenzo Baldi; Bernard Mourrain
Published in: Mathematical Programming, 2023, ISSN 1436-4646
Publisher: Springers
DOI: 10.1007/s10107-022-01877-6

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

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

Bounding the separable rank via polynomial optimization

Author(s): Sander Gribling; Monique Laurent; Andries Steenkamp
Published in: Linear Algebra and its Applications, Issue 39, 2022, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2022.04.010

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

Author(s): Monique Laurent; Luis Felipe Vargas
Published in: SIAM Journal on Optimization, Issue Volume 32, Issue 2, June 2022, 2022, ISSN 1095-7189
Publisher: SIAM
DOI: 10.48550/arxiv.2103.01574

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

Author(s): Schlosser, Corbinian; Korda, Milan
Published in: Congrès SMAI 20, Issue 9, 2020
Publisher: Arxiv
DOI: 10.48550/arxiv.2012.05572

Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients

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

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

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

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

Author(s): Ferguson, Andrew; Le, Huu Phuoc
Published in: ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Issue 9, 2022
Publisher: ACM
DOI: 10.1145/3476446.3536182

Polynomial description for the T-Orbit Spaces of Multiplicative Actions

Author(s): Hubert, Evelyne; Metzlaff, Tobias; Riener, Cordian
Published in: ACM Communications in Computer Algebra, Issue 12, 2022, ISSN 1932-2240
Publisher: ACM
DOI: 10.1145/3572867.3572879

On tensors that are determined by their singular tuples

Author(s): Ettore Teixeira Turatti
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 68, 2022, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/21m1412980

On the solution existence and stability of polynomial optimization problems

Author(s): Vu, Trung-Hieu
Published in: Optimization Letters, 2022, ISSN 1862-4480
Publisher: Springers
DOI: 10.48550/arxiv.1808.06100

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

Author(s): Victor Magron; Mohab Safey El Din; Trung-Hieu Vu
Published in: SIAM Journal on Optimization, 2023, ISSN 1095-7189
Publisher: SIAM
DOI: 10.1137/21m1436245

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

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

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

Author(s): Trung-Hieu Vu
Published in: Set-Valued and Variational Analysis volume, 2022, ISSN 1877-0541
Publisher: Springers
DOI: 10.1007/s11228-022-00637-0

Sparsity Structures for Koopman and Perron--Frobenius Operators

Author(s): Corbinian Schlosser; Milan Korda
Published in: SIAM Journal on Applied Dynamical Systems, Issue Volume 21Issue 3pp. 1663-2296, 2021, ISSN 1536-0040
Publisher: 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

Author(s): Etienne De Klerk; Felix Kirschner
Published in: Optimization Letters, 2022, ISSN 1862-4480
Publisher: Springers
DOI: 10.1007/s11590-022-01851-3

Towards fast one-block quantifier elimination through generalised critical values

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

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

Author(s): Levandovskyy, Viktor; Metzlaff, Tobias; Zeid, Karim,
Published in: Journal of Symbolic Computation, Issue Volume 115, March–April 2023, 2020, Page(s) Pages 201-222, ISSN 0747-7171
Publisher: Academic Press
DOI: 10.1016/j.jsc.2022.08.007

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

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

Conic Optimization with Applications in Finance and Approximation Theory

Author(s): Felix Kirschner
Published in: 2023, ISBN 9789056687090
Publisher: Tilburg University
DOI: 10.26116/x0f5-4k25

Crystallographic groups and Chebyshev polynomials in global optimization

Author(s): Tobias Metzlaff
Published in: 2022
Publisher: Inria

Effective representations in real algebraic geometry and polynomial optimization

Author(s): Lorenzo Baldi
Published in: 2022
Publisher: Inria Université Cote d'Azur

Exact Algorithms for Polynomial Optimisation

Author(s): Andrew Ferguson
Published in: 2022
Publisher: Sorbonne University

Certified Polynomial Optimization Based on Exact Sum of Squares Decompositions

Author(s): Vu Trung Hieu
Published in: 2022
Publisher: Hal

Combinatorics of Reflection Groups and Real Algebraic Geometry

Author(s): Debus, Sebastian
Published in: Issue 2, 2022
Publisher: The Arctic University of Norway

Singular vector tuples and their geometry

Author(s): Ettore Teixeira Turatti
Published in: 2022
Publisher: University of Florence

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

Author(s): Vargas, Luis,; Laurent, Monique
Published in: POEMA Book - Polynomial Optimization, Moments, and Applications, Issue 69, 2023
Publisher: Springer
DOI: 10.48550/arxiv.2302.04690

Polynomial optimization in geometric modeling

Author(s): Soodeh Habibi, Michal Kočvara, Bernard Mourrain
Published in: POEMA Book - Polynomial Optimization, Moments, and Applications, 2023
Publisher: Springer

Matrix factorization ranks via polynomial optimization

Author(s): Steenkamp, Andries
Published 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
Publisher: Arxiv
DOI: 10.48550/arxiv.2302.09994

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