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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

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

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Publications

Exact Moment Representation in Polynomial Optimization

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

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

Author(s): Schlosser, Corbinian; Korda, Milan
Published in: 2020, 9, 2020
Publisher: N/A

On the solution existence and stability of polynomial optimization problems

Author(s): Vu, Trung-Hieu
Published in: https://hal.archives-ouvertes.fr/hal-03002431, 4, 2020
Publisher: N/A

Reflection groups and cones of sums of squares

Author(s): Debus, Sebastian; Riener, Cordian
Published in: 2020, 8, 2020
Publisher: N/A

Computing real radicals by moment optimization

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

Converging outer approximations to global attractors using semidefinite programming

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

A second order cone characterization for sums of nonnegative circuits

Author(s): Magron, Victor; Wang, Jie
Published in: 2020, 1, 2020
Publisher: Hal

TSSOS: A Moment-SOS hierarchy that exploits term sparsity

Author(s): Wang, Jie; Magron, Victor; Lasserre, Jean-Bernard
Published in: 2020, 1, 2020
Publisher: Hal

Computing controlled invariant sets from data using convex optimization

Author(s): Korda, Milan
Published in: https://hal.archives-ouvertes.fr/hal-02398027, 1, 2019
Publisher: Hal

Computing the Hausdorff boundary measure of semi-algebraic sets

Author(s): Lasserre, Jean-Bernard; Magron, Victor
Published in: 2020, 1, 2020
Publisher: Hal

A sparse version of Reznick's Positivstellensatz

Author(s): Mai, N. H. A.; Magron, Victor; Lasserre, Jean-Bernard
Published in: 2020, 1, 2020
Publisher: Hal

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

Author(s): Philippe Moustrou, Cordian Riener, Hugues Verdure
Published in: 2019
Publisher: Hal

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

Author(s): Etienne de Klerk, Monique Laurent
Published in: 2019
Publisher: Hal

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

Author(s): Levandovskyy, Viktor; Metzlaff, Tobias; Zeid, Karim,
Published in: 2020, 10, 2020
Publisher: N/A

Binary forms of suprageneric rank and the multiple root loci

Author(s): Nevado, Alejandro González; Turatti, Ettore Teixeira
Published in: 2020, 11, 2020
Publisher: N/A

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

Author(s): Brosch, Daniel; Laurent, Monique; Steenkamp, Andries
Published in: 13, 2020
Publisher: N/A

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

Computing the volume of compact semi-algebraic sets

Author(s): Lairez, Pierre; Mezzarobba, Marc; Safey El Din, Mohab
Published in: ISSAC 2019, 2019
Publisher: ISAAC

Computing minimal Gorenstein covers

Author(s): Juan Elias, Roser Homs, Bernard Mourrain
Published in: Journal of Pure and Applied Algebra, 2019
Publisher: Elsevier

Computing real radicals and S-radicals of polynomial systems

Author(s): Mohab Safey El Din, Zhi-Hong Yang, Lihong Zhi
Published in: Journal of Symbolic Computation, 2019
Publisher: Elsevier

Computing minimal Gorenstein covers

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

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, 54/3, 2020, Page(s) 109-113, ISSN 1932-2240
Publisher: ACM Communications in Computer Algebra
DOI: 10.1145/3457341.3457348

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

Author(s): Etienne de Klerk, Monique Laurent
Published in: World Women in Mathematics 2018 - Proceedings of the First World Meeting for Women in Mathematics (WM)², 20, 2019, Page(s) 17-56, ISBN 978-3-030-21169-1
Publisher: 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

Author(s): Etienne de Klerk, Monique Laurent
Published in: 2019
Publisher: World Women in Mathematics 2018, 2019