84 citations · 342 across the 90 of their papers we have counts for
105 papers
The bulk spectral gap is certifiable from above but uncomputable from below
Xiangling Xu, Matthias Schötz, Jie Wang +4
Determining spectral gaps in the thermodynamic limit is a central challenge in quantum many-body physics. When a fixed boundary condition is imposed, this problem is undecidable: n…
Sums of squares in polynomial time
Nikolas Gärtner, Victor Magron, Frank Vallentin
In this paper, we analyze the bit complexity of deciding whether a given polynomial can be represented as a sum of squares of polynomials. We show that the weak membership problem…
Quantitative semidefinite certificates for ground-state energies of Pauli Hamiltonians
Igor Klep, Nando Leijenhorst, Victor Magron
The -local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchie…
Duality attainment and strict feasibility of the generalized moment problem and its relaxations
Sami Halaseh, Victor Magron, Mateusz Skomra
The generalized moment problem (GMP) is an infinite dimensional linear problem over the cone of finite nonnegative Borel measures. When a GMP instance involves finitely many polyno…
Robust self-testing with CHSH mod 3
Igor Klep, Nando Leijenhorst, Victor Magron
The CHSH mod 3 Bell inequality is a natural testbed for higher-dimensional quantum nonlocality, yet its maximal quantum violation and self-testing properties have remained unresolv…
Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization
Jie Wang, David Jansen, Irénée Frerot +3
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard variational approaches posit a wave-function ansatz and…
The Effective Lasserre's Perturbative Positivstellensatz
Igor Klep, Victor Magron, Matthias Schötz
We study sum-of-squares (SOS) certificates for nonnegative polynomials on and their implications for polynomial optimization over unbounded domains. Building on…
Certified bounds on optimization problems in quantum theory
Younes Naceur, Jie Wang, Victor Magron +1
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitou…
Inclusion constants for free spectrahedra with applications to quantum incompatibility
Andreas Bluhm, Eric Evert, Igor Klep +2
Building on the matrix cube problem, inclusions of free spectrahedra have been used successfully to obtain relaxations of hard spectrahedral inclusion problems. The quality of such…
Finite Convergence of the Moment-SOS Hierarchy on the Product of Spheres
Sami Halaseh, Victor Magron, Mateusz Skomra
We study the polynomial optimization problem of minimizing a multihomogeneous polynomial over the product of spheres. This polynomial optimization problem models the tensor optimiz…
Exploiting Term Sparsity in Symmetry-Adapted Basis for Polynomial Optimization
Igor Klep, Victor Magron, Tobias Metzlaff +1
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programmi…
Moment-SOS hierarchies for arrow-type polynomial matrix inequalities with applications to structural optimization
Marouan Handa, Marek Tyburec, Giovanni Fantuzzi +2
The Arrow Decomposition (AD) technique, initially introduced in [Mathematical Programming 190(1-2) (2021), pp 105-134], demonstrated superior scalability over the classical chordal…
Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
Srećko Đurašinović, Jean-Bernard Lasserre, Victor Magron
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settin…
Approximating the order 2 quantum Wasserstein distance using the moment-SOS hierarchy
Saroj Prasad Chhatoi, Victor Magron
Optimal transport theory has recently been extended to quantum settings, where the density matrices generalize the probability measures. In this paper, we study the computational a…
Convergence rates for polynomial optimization on set products
Victor Magron
We consider polynomial optimization problems on Cartesian products of basic compact semialgebraic sets. The solution of such problems can be approximated as closely as desired by h…
Detecting Destabilizing Nonlinearities in Absolute Stability Analysis of Discrete-Time Feedback Systems
Hibiki Gyotoku, Tsuyoshi Yuno, Yoshio Ebihara +3
This paper is concerned with the absolute stability analysis of discrete-time feedback systems with slope-restricted nonlinearities. By employing static O'Shea-Zames-Falb multiplie…
Leveraging Christoffel-Darboux Kernels to Strengthen Moment-SOS Relaxations
Srećko Ðurašinović, Perla Azzi, Jean-Bernard Lasserre +3
The classical Moment-SOS hierarchy allows one to approximate the global minimum of a polynomial optimization problem through semidefinite relaxations of increasing accuracy. For ma…
On the Complexity of p-Order Cone Programs
Víctor Blanco, Victor Magron, Miguel Martínez-Antón
This manuscript explores novel complexity results for the feasibility problem over -order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the int…
Positivity of state, trace, and moment polynomials, and applications in quantum information
Felix Huber, Victor Magron, Jurij Volčič
State, trace, and moment polynomials are polynomial expressions in several operator or random variables and positive functionals on their products (states, traces or expectations).…
On Dual of LMIs for Absolute Stability Analysis of Nonlinear Feedback Systems with Static O'Shea-Zames-Falb Multipliers
Hibiki Gyotoku, Tsuyoshi Yuno, Yoshio Ebihara +3
This study investigates the absolute stability criteria based on the framework of integral quadratic constraint (IQC) for feedback systems with slope-restricted nonlinearities. In…
Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization
Jianting Yang, Srećko Ðurašinović, Jean-Bernard Lasserre +2
This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and…
Slow convergence of the moment-SOS hierarchy for an elementary polynomial optimization problem
Didier Henrion, Adrien Le Franc, Victor Magron
We describe a parametric univariate quadratic optimization problem for which the moment-SOS hierarchy has finite but increasingly slow convergence when the parameter tends to its l…
LMI hierarchies for stability analysis of ReLU feedback systems
Victor Magron, Yoshio Ebihara, Shingo Nishinaka +4
We consider the stability analysis of feedback systems with rectified linear unit (ReLU) activations, and model this problem with polynomial optimization. Stability can be certifie…
Upper bound hierarchies for noncommutative polynomial optimization
Igor Klep, Victor Magron, Gaël Massé +1
This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-Mc…