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Semidefinite Approximations of Reachable Sets for Discrete-time Polynomial...
Victor Magron, Pierre-Loïc Garoche, Didier Henrion, Xavier Thirioux: Semidefinite Approximations of Reachable Sets for Discrete-time Polynomial Systems. SIAM J. Control. Optim. 57(4): 2799-2820 (2019)
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Algorithms for weighted sum of squares decomposition of non-negative...
Victor Magron, Mohab Safey El Din, Markus Schweighofer: Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials. J. Symb. Comput. 93: 200-220 (2019)
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SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone...
Victor Magron, Jie Wang: SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone Programming. CoRR abs/2012.07903 (2020)
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Computer-assisted proofs for Lyapunov stability via Sums of Squares...
Grigory Devadze, Victor Magron, Stefan Streif: Computer-assisted proofs for Lyapunov stability via Sums of Squares certificates and Constructive Analysis. CoRR abs/2006.09884 (2020)
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CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization.
Jie Wang, Victor Magron, Jean B. Lasserre, Ngoc Hoang Anh Mai: CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization. CoRR abs/2005.02828 (2020)
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Polynomial Optimization for Bounding Lipschitz Constants of Deep Networks.
Tong Chen, Jean-Bernard Lasserre, Victor Magron, Edouard Pauwels: Polynomial Optimization for Bounding Lipschitz Constants of Deep Networks. CoRR abs/2002.03657 (2020)
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Semialgebraic Optimization for Lipschitz Constants of ReLU Networks.
Tong Chen, Jean B. Lasserre, Victor Magron, Edouard Pauwels: Semialgebraic Optimization for Lipschitz Constants of ReLU Networks. NeurIPS 2020
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A second order cone characterization for sums of nonnegative circuits.
Jie Wang, Victor Magron: A second order cone characterization for sums of nonnegative circuits. ISSAC 2020: 450-457
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Computing the Hausdorff Boundary Measure of Semialgebraic Sets.
Jean B. Lasserre, Victor Magron: Computing the Hausdorff Boundary Measure of Semialgebraic Sets. SIAM J. Appl. Algebra Geom. 4(3): 441-469 (2020)
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Optimal control of linear PDEs using occupation measures and SDP relaxations.
Victor Magron, Christophe Prieur: Optimal control of linear PDEs using occupation measures and SDP relaxations. IMA J. Math. Control. Inf. 37(1): 159-174 (2020)
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Sum of Squares Decompositions of Polynomials over their Gradient Ideals with...
Victor Magron, Mohab Safey El Din, Trung Hieu Vu: Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients. CoRR abs/2107.11825 (2021)
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TSSOS: a Julia library to exploit sparsity for large-scale polynomial...
Victor Magron, Jie Wang: TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization. CoRR abs/2103.00915 (2021)
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Semialgebraic Representation of Monotone Deep Equilibrium Models and...
Tong Chen, Jean B. Lasserre, Victor Magron, Edouard Pauwels: Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certification. NeurIPS 2021: 27146-27159
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The Constant Trace Property in Noncommutative Optimization.
Ngoc Hoang Anh Mai, Abhishek Bhardwaj, Victor Magron: The Constant Trace Property in Noncommutative Optimization. ISSAC 2021: 297-304
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Stability Analysis of Recurrent Neural Networks by IQC with Copositive...
Yoshio Ebihara, Hayato Waki, Victor Magron, Ngoc Hoang Anh Mai, Dimitri Peaucelle, Sophie Tarbouriech: Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers. CDC 2021:...
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SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS...
Jie Wang, Martina Maggio, Victor Magron: SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS Decompositions. ACC 2021: 2254-2259
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Minimizing Rational Functions: A Hierarchy of Approximations via Pushforward...
Jean-Bernard Lasserre, Victor Magron, Swann Marx, Olivier Zahm: Minimizing Rational Functions: A Hierarchy of Approximations via Pushforward Measures. SIAM J. Optim. 31(3): 2285-2306 (2021)
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Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with...
Jie Wang, Victor Magron, Jean-Bernard Lasserre: Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with Chordal Extension. SIAM J. Optim. 31(1): 114-141 (2021)
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TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity.
Jie Wang, Victor Magron, Jean-Bernard Lasserre: TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity. SIAM J. Optim. 31(1): 30-58 (2021)
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On exact Reznick, Hilbert-Artin and Putinar's representations.
Victor Magron, Mohab Safey El Din: On exact Reznick, Hilbert-Artin and Putinar's representations. J. Symb. Comput. 107: 221-250 (2021)
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l2 induced norm analysis of discrete-time LTI systems for nonnegative input...
Yoshio Ebihara, Hayato Waki, Victor Magron, Ngoc Hoang Anh Mai, Dimitri Peaucelle, Sophie Tarbouriech: l2 induced norm analysis of discrete-time LTI systems for nonnegative input signals and its...
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Exploiting term sparsity in noncommutative polynomial optimization.
Jie Wang, Victor Magron: Exploiting term sparsity in noncommutative polynomial optimization. Comput. Optim. Appl. 80(2): 483-521 (2021)
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The quest of modeling, certification and efficiency in polynomial...
Victor Magron: The quest of modeling, certification and efficiency in polynomial optimization. (La quête de modélisation, de certification et d'efficacité en optimisation polynomiale). Paul Sabatier...
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Tractable hierarchies of convex relaxations for polynomial optimization on...
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre, Kim-Chuan Toh: Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant. CoRR abs/2209.06175 (2022)
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Sparse Polynomial Optimization: Theory and Practice.
Victor Magron, Jie Wang: Sparse Polynomial Optimization: Theory and Practice. CoRR abs/2208.11158 (2022)
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Exact SOHS decompositions of trigonometric univariate polynomials with...
Victor Magron, Mohab Safey El Din, Markus Schweighofer, Trung Hieu Vu: Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients. CoRR abs/2202.06544 (2022)
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Stability Analysis of Recurrent Neural Networks by IQC with Copositive...
Yoshio Ebihara, Hayato Waki, Victor Magron, Ngoc Hoang Anh Mai, Dimitri Peaucelle, Sophie Tarbouriech: Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers. CoRR...
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Exact SOHS Decompositions of Trigonometric Univariate Polynomials with...
Victor Magron, Mohab Safey El Din, Markus Schweighofer, Trung Hieu Vu: Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients. ISSAC 2022: 325-332
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L2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive...
Yoshio Ebihara, Hayato Motooka, Hayato Waki, Noboru Sebe, Victor Magron, Dimitri Peaucelle, Sophie Tarbouriech: L2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and...
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CS-TSSOS: Correlative and Term Sparsity for Large-Scale Polynomial Optimization.
Jie Wang, Victor Magron, Jean B. Lasserre, Ngoc Hoang Anh Mai: CS-TSSOS: Correlative and Term Sparsity for Large-Scale Polynomial Optimization. ACM Trans. Math. Softw. 48(4): 42:1-42:26 (2022)
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Exploiting Constant Trace Property in Large-scale Polynomial Optimization.
Ngoc Hoang Anh Mai, Jean B. Lasserre, Victor Magron, Jie Wang: Exploiting Constant Trace Property in Large-scale Polynomial Optimization. ACM Trans. Math. Softw. 48(4): 40:1-40:39 (2022)
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Positivity certificates and polynomial optimization on non-compact...
Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron: Positivity certificates and polynomial optimization on non-compact semialgebraic sets. Math. Program. 194(1): 443-485 (2022)
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Sparse noncommutative polynomial optimization.
Igor Klep, Victor Magron, Janez Povh: Sparse noncommutative polynomial optimization. Math. Program. 193(2): 789-829 (2022)
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Exploiting Sparsity in Complex Polynomial Optimization.
Jie Wang, Victor Magron: Exploiting Sparsity in Complex Polynomial Optimization. J. Optim. Theory Appl. 192(1): 335-359 (2022)
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On the complexity of Putinar-Vasilescu's Positivstellensatz.
Ngoc Hoang Anh Mai, Victor Magron: On the complexity of Putinar-Vasilescu's Positivstellensatz. J. Complex. 72: 101663 (2022)
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Stability of Linear Systems Under Extended Weakly-Hard Constraints.
Nils Vreman, Paolo Pazzaglia, Victor Magron, Jie Wang, Martina Maggio: Stability of Linear Systems Under Extended Weakly-Hard Constraints. IEEE Control. Syst. Lett. 6: 2900-2905 (2022)
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A sublevel moment-SOS hierarchy for polynomial optimization.
Tong Chen, Jean-Bernard Lasserre, Victor Magron, Edouard Pauwels: A sublevel moment-SOS hierarchy for polynomial optimization. Comput. Optim. Appl. 81(1): 31-66 (2022)
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Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation...
Yoshio Ebihara, Xin Dai, Victor Magron, Dimitri Peaucelle, Sophie Tarbouriech: Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification. CoRR...
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Convergence rates for sums-of-squares hierarchies with correlative sparsity.
Milan Korda, Victor Magron, Rodolfo Rios-Zertuche: Convergence rates for sums-of-squares hierarchies with correlative sparsity. CoRR abs/2303.14824 (2023)
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Peak Estimation of Time Delay Systems using Occupation Measures.
Jared Miller, Milan Korda, Victor Magron, Mario Sznaier: Peak Estimation of Time Delay Systems using Occupation Measures. CoRR abs/2303.12863 (2023)
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Pourchet's theorem in action: decomposing univariate nonnegative polynomials...
Victor Magron, Przemyslaw Koprowski, Tristan Vaccon: Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares. CoRR abs/2302.02202 (2023)
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Pourchet's theorem in action: decomposing univariate nonnegative polynomials...
Przemyslaw Koprowski, Victor Magron, Tristan Vaccon: Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares. ISSAC 2023: 425-433
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Peak Estimation of Time Delay Systems Using Occupation Measures.
Jared Miller, Milan Korda, Victor Magron, Mario Sznaier: Peak Estimation of Time Delay Systems Using Occupation Measures. CDC 2023: 5294-5300
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Exploiting Term Sparsity in Moment-SOS Hierarchy for Dynamical Systems.
Jie Wang, Corbinian Schlosser, Milan Korda, Victor Magron: Exploiting Term Sparsity in Moment-SOS Hierarchy for Dynamical Systems. IEEE Trans. Autom. Control. 68(12): 8232-8237 (2023)
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Sum of Squares Decompositions of Polynomials over their Gradient Ideals with...
Victor Magron, Mohab Safey El Din, Trung Hieu Vu: Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients. SIAM J. Optim. 33(1): 63-88 (2023)
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Correlations constrained by composite measurements.
John H. Selby, Ana Belén Sainz, Victor Magron, Lukasz Czekaj, Michal Horodecki: Correlations constrained by composite measurements. Quantum 7: 1080 (2023)
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A hierarchy of spectral relaxations for polynomial optimization.
Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron: A hierarchy of spectral relaxations for polynomial optimization. Math. Program. Comput. 15(4): 651-701 (2023)
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A Sparse Version of Reznick's Positivstellensatz.
Ngoc Hoang Anh Mai, Victor Magron, Jean B. Lasserre: A Sparse Version of Reznick's Positivstellensatz. Math. Oper. Res. 48(2): 812-833 (2023)
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SONC optimization and exact nonnegativity certificates via second-order cone...
Victor Magron, Jie Wang: SONC optimization and exact nonnegativity certificates via second-order cone programming. J. Symb. Comput. 115: 346-370 (2023)
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Sparse Polynomial Optimization - Theory and Practice.
Victor Magron, Jie Wang: Sparse Polynomial Optimization - Theory and Practice. Series on Optimization and its Applications 5, WorldScientific 2023, ISBN 9781800612945, pp. 1-224
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