People

Victor Magron

Victor Magron

Research team

POP : Polynomial OPtimization

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Latest publications

2024

Preprints, Working Papers, ...

Igor Klep, Victor Magron, Gaël Massé, Jurij Volčič. Upper bound hierarchies for noncommutative polynomial optimization. 2024. ⟨hal-04440949⟩

Yoshio Ebihara, Noboru Sebe, Hayato Waki, Dimitri Peaucelle, Sophie Tarbouriech, et al.. Induced Norm Analysis of Linear Systems for Nonnegative Input Signals. 2024. ⟨hal-04438031⟩

2023

Journal articles

Milan Korda, Monique Laurent, Victor Magron, Andries Steenkamp. Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks. Mathematical Programming, 2023, ⟨10.1007/s10107-023-01993-x⟩. ⟨hal-03782934⟩

Serban Belinschi, Victor Magron, Victor Vinnikov. Noncommutative Christoffel-Darboux Kernels. Transactions of the American Mathematical Society, 2023, 376, pp.181-230. ⟨10.1090/tran/8648⟩. ⟨hal-03433869⟩

Victor Magron, Mohab Safey El Din, Trung-Hieu Vu. Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients. SIAM Journal on Optimization, 2023, 33 (1), ⟨10.1137/21M1436245⟩. ⟨hal-03312392⟩

Didier Henrion, Felix Kirschner, Etienne de Klerk, Milan Korda, Jean-Bernard Lasserre, et al.. Revisiting semidefinite programming approaches to options pricing: complexity and computational perspectives. INFORMS Journal on Computing, 2023, 35 (2), pp.265-517. ⟨hal-03429272v2⟩

Adrien Le Franc, Victor Magron, Jean-Bernard Lasserre, Manuel Ruiz, Patrick Panciatici. Minimal Sparsity for Second-Order Moment-SOS Relaxations of the AC-OPF Problem. IEEE Transactions on Power Systems, 2023, pp.1 - 10. ⟨10.1109/TPWRS.2023.3333691⟩. ⟨hal-04110742v2⟩

Victor Magron, Jie Wang. SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone Programming. Journal of Symbolic Computation, 2023, 115, pp.346-370. ⟨10.1016/j.jsc.2022.08.002⟩. ⟨hal-03070864⟩

Books

Victor Magron, Jie Wang. Sparse Polynomial Optimization: Theory and Practice. World Scientific Press. 2023, Series on Optimization and Its Applications, 978-1-80061-294-5. ⟨hal-03760501⟩

Preprints, Working Papers, ...

Victor Magron, Przemysław Koprowski, Tristan Vaccon. Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares. 2023. ⟨hal-03976836⟩

Jie Wang, Jacopo Surace, Irénée Frérot, Benoît Legat, Marc-Olivier Renou, et al.. Certifying ground-state properties of many-body systems. 2023. ⟨hal-04264341⟩

John H. Selby, Ana Belén Sainz, Victor Magron, Łukasz Czekaj, Michał Horodecki. Correlations constrained by composite measurements. 2023. ⟨hal-04117038⟩

Jared Miller, Milan Korda, Victor Magron, Mario Sznaier. Peak Estimation of Time Delay Systems using Occupation Measures. 2023. ⟨hal-04047493⟩

Igor Klep, Victor Magron, Jurij Volčič. Sums of squares certificates for polynomial moment inequalities. 2023. ⟨hal-04125262⟩

Igor Klep, Victor Magron, Jurij Volčič, Jie Wang. State polynomials: positivity, optimization and nonlinear Bell inequalities. 2023. ⟨hal-03964830⟩

Milan Korda, Victor Magron, Rodolfo Rios-Zertuche. Convergence rates for sums-of-squares hierarchies with correlative sparsity. 2023. ⟨hal-04049383⟩

Victor Magron. Exploiting sparsity in polynomial optimization. École thématique. Luminy, France. 2023. ⟨hal-04193936⟩

Yoshio Ebihara, Xin Dai, Victor Magron, Dimitri Peaucelle, Sophie Tarbouriech. Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification. 2023. ⟨hal-04247204⟩

Ngoc Hoang Anh Mai, Victor Magron. Sums of squares representations on singular loci. 2023. ⟨hal-04023980⟩

Jie Wang, Victor Magron. A real moment-HSOS hierarchy for complex polynomial optimization with real coefficients. 2023. ⟨hal-04189927⟩

Nicolas Augier, Didier Henrion, Milan Korda, Victor Magron. Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations. 2023. ⟨hal-04159304⟩

2022

Journal articles

Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron, Jie Wang. Exploiting constant trace property in large-scale polynomial optimization. ACM Transactions on Mathematical Software, 2022, 48 (4), pp.1-39. ⟨10.1145/3555309⟩. ⟨hal-03079000⟩

Felix Huber, Igor Klep, Victor Magron, Jurij Volčič. Dimension-free entanglement detection in multipartite Werner states. Communications in Mathematical Physics, 2022, 396, pp.1051-1070. ⟨10.1007/s00220-022-04485-9⟩. ⟨hal-03322991⟩

Jie Wang, Victor Magron. Exploiting Sparsity in Complex Polynomial Optimization. Journal of Optimization Theory and Applications, 2022, 192, pp.335-359. ⟨10.1007/s10957-021-01975-z⟩. ⟨hal-03178832⟩

N. H. A. Mai, Victor Magron, Jean-Bernard Lasserre. A sparse version of Reznick's Positivstellensatz. Mathematics of Operations Research, 2022, ⟨10.1287/moor.2022.1284⟩. ⟨hal-02477339⟩

Ngoc Hoang Anh Mai, Victor Magron. On the complexity of Putinar-Vasilescu's Positivstellensatz. Journal of Complexity, 2022, ⟨10.1016/j.jco.2022.101663⟩. ⟨hal-03820206⟩

Tong Chen, Jean-Bernard Lasserre, Victor Magron, Edouard Pauwels. A Sublevel Moment-SOS Hierarchy for Polynomial Optimization. Computational Optimization and Applications, 2022, 81 (1), pp.31-66. ⟨10.1007/s10589-021-00325-z⟩. ⟨hal-03109978⟩

Jie Wang, Victor Magron, Jean-Bernard Lasserre. Certifying Global Optimality of AC-OPF Solutions via the CS-TSSOS Hierarchy. Electric Power Systems Research, 2022, 213, pp.108683. ⟨10.1016/j.epsr.2022.108683⟩. ⟨hal-03351160⟩

Nils Vreman, Paolo Pazzaglia, Jie Wang, Victor Magron, Martina Maggio. Stability of Linear Systems under Extended Weakly-Hard Constraints. IEEE Control Systems Letters, 2022, 6, pp.2900-2905. ⟨10.1109/LCSYS.2022.3179960⟩. ⟨hal-03127108⟩

Conference papers

Yoshio Ebihara, Hayato Waki, Noboru Sebe, Victor Magron, Dimitri Peaucelle, et al.. L 2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming. European Control Conference (ECC 2022), Jul 2022, Londres, United Kingdom. ⟨10.23919/ECC55457.2022.9838085⟩. ⟨hal-03740522⟩

Victor Magron, Mohab Safey El Din, Markus Schweighofer, Trung Hieu Vu. Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients. International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2022, Lille, France. ⟨hal-03575157⟩

Preprints, Working Papers, ...

Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre, Kim-Chuan Toh. Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant. 2022. ⟨hal-03776853⟩

Milan Korda, Jean-Bernard Lasserre, Alexey Lazarev, Victor Magron, Simone Naldi. Urysohn in action: separating semialgebraic sets by polynomials. 2022. ⟨hal-03712510⟩

Victor Magron, Ngoc Hoang Anh Mai, Yoshio Ebihara, Hayato Waki. Tractable semidefinite bounds of positive maximal singular values. 2022. ⟨hal-03580048⟩

2021

Journal articles

Jean-Bernard Lasserre, Victor Magron, Swann Marx, Olivier Zahm. Minimizing rational functions: a hierarchy of approximations via pushforward measures. SIAM Journal on Optimization, 2021, 31 (3), pp.2285-2306. ⟨10.1137/20M138541X⟩. ⟨hal-03053386⟩

Jie Wang, Victor Magron, Jean-Bernard Lasserre. TSSOS: A Moment-SOS hierarchy that exploits term sparsity. SIAM Journal on Optimization, 2021, 31 (1), pp.30--58. ⟨10.1137/19M1307871⟩. ⟨hal-02448389⟩

Jie Wang, Victor Magron, Jean-Bernard Lasserre. Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension. SIAM Journal on Optimization, 2021, ⟨10.1137/20M1323564⟩. ⟨hal-02502131⟩

Yoshio Ebihara, Hayato Waki, Victor Magron, Ngoc Hoang Anh Mai, Dimitri Peaucelle, et al.. $l_2$ Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative Input Signals and Its Application to Stability Analysis of Recurrent Neural Networks. European Journal of Control, 2021, 62, pp.99-104. ⟨10.1016/j.ejcon.2021.06.022⟩. ⟨hal-03026445⟩

Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron. Positivity certificates and polynomial optimization on non-compact semialgebraic sets. Mathematical Programming, Series A, 2021, ⟨10.1007/s10107-021-01634-1⟩. ⟨hal-02382059⟩

Victor Magron, Mohab Safey El Din. On Exact Reznick, Hilbert-Artin and Putinar's Representations. Journal of Symbolic Computation, 2021, 107, pp.221-250. ⟨10.1016/j.jsc.2021.03.005⟩. ⟨hal-01935727⟩

Igor Klep, Victor Magron, Jurij Volčič. Optimization over trace polynomials. Annales Henri Poincaré, 2021, ⟨10.1007/s00023-021-01095-4⟩. ⟨hal-02879621⟩

Jie Wang, Victor Magron. Exploiting term sparsity in Noncommutative Polynomial Optimization. Computational Optimization and Applications, 2021, 80, pp.483-521. ⟨10.1007/s10589-021-00301-7⟩. ⟨hal-02967839⟩

Conference papers

Victor Magron, Yoshio Ebihara, Hayato Waki, Ngoc Hoang Anh Mai, Dimitri Peaucelle, et al.. Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers. Control and Decision Conference (CDC) 2021, Dec 2021, Austin, United States. ⟨hal-03564261⟩

Ngoc Hoang Anh Mai, Abhishek Bhardwaj, Victor Magron. The Constant Trace Property in Noncommutative Optimization. International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint Petersbourg, Russia. ⟨10.1145/3452143.3465516⟩. ⟨hal-03130967⟩

Jie Wang, Martina Maggio, Victor Magron. SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS Decompositions. 2021 American Control Conference (ACC), May 2021, New Orleans, United States. ⟨10.23919/ACC50511.2021.9483347⟩. ⟨hal-02923348⟩

Victor Magron, Jie Wang. TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization. Effective Methods in Algebraic Geometry, Jun 2021, Tromso, Norway. ⟨hal-03155742⟩

Tong Chen, Jean-Bernard Lasserre, Victor Magron, Edouard Pauwels. Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certification. Advances in Neural Information Processing Systems, Dec 2021, Online, France. ⟨hal-03265346⟩

PhD thesis, HDR

Victor Magron. The quest of modeling, certification and efficiency in polynomial optimization. Automatic Control Engineering. Université Toulouse 3 Paul Sabatier, 2021. ⟨tel-03246038⟩

Preprints, Working Papers, ...

Victor Magron, Jie Wang, Corbinian Schlosser, Milan Korda. Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems. 2021. ⟨hal-03439458⟩

Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre. A hierarchy of spectral relaxations for polynomial optimization. 2021. ⟨hal-03149938⟩

Abhishek Bhardwaj, Igor Klep, Victor Magron. Noncommutative Polynomial Optimization. 2021. ⟨hal-03333504⟩

2020

Journal articles

Victor Magron, Christophe Prieur. Optimal Control of Linear PDEs using Occupation Measures and SDP Relaxations. IMA Journal of Mathematical Control and Information, 2020, 37 (1), pp.159-174. ⟨10.1093/imamci/dny044⟩. ⟨hal-01966782⟩

Jean-Bernard Lasserre, Victor Magron. Computing the Hausdorff boundary measure of semi-algebraic sets. SIAM Journal on Applied Algebra and Geometry, 2020, 4 (3), pp.441-469. ⟨10.1137/20M1314392⟩. ⟨hal-02448149⟩

Igor Klep, Victor Magron, Janez Povh. Sparse Noncommutative Polynomial Optimization. Mathematical Programming, Series A, 2020, ⟨10.1007/s10107-020-01610-1⟩. ⟨hal-02278767⟩

Conference papers

Tong Chen, Jean-Bernard Lasserre, Victor Magron, Edouard Pauwels. Semialgebraic Optimization for Lipschitz Constants of ReLU Networks. Conference on Neural Information Processing Systems, Dec 2020, Vancouver, Canada. ⟨hal-02940488⟩

Victor Magron, Jie Wang. A second order cone characterization for sums of nonnegative circuits. 45th International Symposium on Symbolic and Algebraic Computation (ISSAC'20), Jul 2020, Virtual, Greece. pp.450-457, ⟨10.1145/3373207.3404033⟩. ⟨hal-02473446⟩

Preprints, Working Papers, ...

Jie Wang, Victor Magron, Jean B Lasserre, Ngoc Hoang Anh Mai. CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization. 2020. ⟨hal-02566472⟩

Grigory Devadze, Victor Magron, Stefan Streif. Computer-assisted proofs for Lyapunov stability via Sums of Squares certificates and Constructive Analysis. 2020. ⟨hal-02873040⟩

2019

Journal articles

Victor Magron, Marcelo Forets, Didier Henrion. Semidefinite Approximations of Invariant Measures for Polynomial Systems. Discrete and Continuous Dynamical Systems - Series B, 2019, 24 (12), pp.6745-6770. ⟨10.3934/dcdsb.2019165⟩. ⟨hal-01828443⟩

Victor Magron, Pierre-Loïc Garoche, Didier Henrion, Xavier Thirioux. Semidefinite Approximations of Reachable Sets for Discrete-time Polynomial Systems. SIAM Journal on Control and Optimization, 2019, 57 (4), pp.2799-2820. ⟨10.1137/17M1121044⟩. ⟨hal-01490897⟩

Victor Magron, Alexandre Rocca, Thao Dang. Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations. IEEE Transactions on Computers, 2019, 68 (7), pp.953-966. ⟨10.1109/TC.2018.2851235⟩. ⟨hal-01956817⟩

Victor Magron, Henning Seidler, Timo de Wolff. EXACT OPTIMIZATION VIA SUMS OF NONNEGATIVE CIRCUITS AND SUMS OF AM/GM EXPONENTIALS. ACM Communications in Computer Algebra, 2019, ⟨10.1145/3326229.3326271⟩. ⟨hal-02006899⟩

Victor Magron, Mohab Safey El Din, Markus Schweighofer. Algorithms for Weighted Sums of Squares Decomposition of Non-negative Univariate Polynomials. Journal of Symbolic Computation, 2019, 93, pp.200-220. ⟨10.1016/j.jsc.2018.06.005⟩. ⟨hal-01538729⟩

Jean-Bernard Lasserre, Victor Magron. In SDP relaxations, inaccurate solvers do robust optimization. SIAM Journal on Optimization, 2019, 29 (3), pp.2128-2145. ⟨10.1137/18M1225677⟩. ⟨hal-01915976⟩

Books

Victor Magron, Alexandre Rocca, Thao Dang. Certified Roundoff Error Bounds Using Bernstein Expansions and Sparse Krivine-Stengle Representations. 68 (7), pp.953-966, 2019, ⟨10.1109/TC.2018.2851235⟩. ⟨hal-02402354⟩

Autres documents

Dimitri Peaucelle, Marie-José Huguet, Yannick Pencolé, Christian Artigues, Emmanuel Hébrard, et al.. Bilan et prospectives 2019 du département Décision & Optimisation du LAAS-CNRS. Rapport LAAS n° 19270. 2019. ⟨hal-02295816⟩

2018

Journal articles

Jean-Bernard Lasserre, Victor Magron. Optimal data fitting: a moment approach. SIAM Journal on Optimization, 2018, 28 (4), pp.3127-3144. ⟨10.1137/18M1170108⟩. ⟨hal-01706850⟩

Victor Magron, Mohab Safey El Din. RealCertify: a Maple package for certifying non-negativity. ACM Communications in Computer Algebra, 2018, 52 (2), pp.34-37. ⟨10.1145/3282678.3282681⟩. ⟨hal-01956812⟩

Victor Magron. Interval Enclosures of Upper Bounds of Roundoff Errors using Semidefinite Programming. ACM Transactions on Mathematical Software, 2018, 44 (4), pp.41:1--41:18. ⟨10.1145/3206430⟩. ⟨hal-01956815⟩

Conference papers

Victor Magron, Mohab Safey El Din. On Exact Polya and Putinar's Representations. ISSAC '18 International Symposium on Symbolic and Algebraic Computation, Jul 2018, New-York, United States. pp.279-286, ⟨10.1145/3208976.3208986⟩. ⟨hal-01720612⟩

2017

Preprints, Working Papers, ...

Victor Magron, Mountassir Farid. A Certified Lower Bounds of Roundoff Errors using Semidefinite Programming. 2017. ⟨hal-01448160⟩

Alexandre Rocca, Victor Magron, Thao Dang. Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations. 2017. ⟨hal-01448167⟩

Assalé Adjé, Pierre-Loïc Garoche, Victor Magron. A Sums-of-Squares Extension of Policy Iterations. 2017. ⟨hal-01133405v2⟩

2015

Journal articles

Victor Magron, Didier Henrion, Jean-Bernard Lasserre. Semidefinite approximations of projections and polynomial images of semialgebraic sets. SIAM Journal on Optimization, 2015, 25 (4), pp. 2143-2164. ⟨hal-01075343v2⟩

Victor Magron, Xavier Allamigeon, Stéphane Gaubert, Benjamin Werner. Formal Proofs for Nonlinear Optimization. Journal of Formalized Reasoning, 2015, 8 (15), pp.1-24. ⟨hal-00985675⟩

Book sections

Assalé Adjé, Pierre-Loïc Garoche, Victor Magron. Property-based Polynomial Invariant Generation Using Sums-of-Squares Optimization. Blazy Sandrine; Jensen Thomas. Static Analysis, Springer Berlin Heidelberg, pp.235-251, 2015, 978-3-662-48287-2. ⟨10.1007/978-3-662-48288-9_14⟩. ⟨hal-01369974⟩

Conference papers

Assalé Adjé, Pierre-Loïc Garoche, Victor Magron. Automatic Synthesis of Piecewise Linear Quadratic Invariants for Programs. Verification Model Checking and Abstract Interpretation 2015 (VMCAI 2015), Jan 2015, Mumbai, India. pp.99-116. ⟨hal-01371514⟩

Assalé Adjé, Pierre-Loïc Garoche, Victor Magron. Property-based Polynomial Invariant Generation Using Sums-Of-Squares . Static Analysis Symposium 2015 (2015), Sep 2015, Saint-Malo, France. pp.235-251. ⟨hal-01371508⟩

Preprints, Working Papers, ...

Assalé Adjé, Pierre-Loïc Garoche, Victor Magron. Property-based Polynomial Invariant Generation using Sums-of-Squares Optimization. 2015. ⟨hal-01134816⟩

2014

Journal articles

Victor Magron, Didier Henrion, Jean-Bernard Lasserre. Approximating Pareto Curves using Semidefinite Relaxations. Operations Research Letters, 2014, 42 (6-7), pp.432-437. ⟨hal-00980625v2⟩

Victor Magron. Error Bounds for Polynomial Optimization over the Hypercube using Putinar type Representations. Optimization Letters, 2014, ⟨10.1007/s11590-014-0797-8⟩. ⟨hal-00983485⟩

Victor Magron, Xavier Allamigeon, Stéphane Gaubert, Benjamin Werner. Certification of real inequalities: templates and sums of squares. Mathematical Programming, 2014, 151 (2), pp.30. ⟨10.1007/s10107-014-0834-5⟩. ⟨hal-01096485⟩

Conference papers

Victor Magron. NLCertify: A Tool for Formal Nonlinear Optimization. International Congress on Mathematical Software (ICMS), Aug 2014, Seoul, South Korea. 6p. ⟨hal-00995686⟩

Preprints, Working Papers, ...

Assalé Adjé, Victor Magron. Polynomial Template Generation using Sum-of-Squares Programming. 2014. ⟨hal-01064305⟩