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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

Publications

Computing the volume of compact semi-algebraic sets

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

Computing minimal Gorenstein covers

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

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

A second order cone characterization for sums of nonnegative circuits

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

TSSOS: A Moment-SOS hierarchy that exploits term sparsity

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

Computing controlled invariant sets from data using convex optimization

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

Computing the Hausdorff boundary measure of semi-algebraic sets

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

A sparse version of Reznick's Positivstellensatz

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

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

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

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

Computing minimal Gorenstein covers

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

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, Issue 20, 2019, Page(s) 17-56
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