Distance to a constitutive tensor isotropy stratum by the Lasserre polynomial optimization method

DOI10.2140/memocs.2023.11.393zbMath1527.90149arXiv2207.04729OpenAlexW4313624390MaRDI QIDQ6082663

Boris Kolev, Rodrigue Desmorat, Perla Azzi, Fabien Priziac

Publication date: 30 November 2023

Published in: Mathematics and Mechanics of Complex Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.04729

zbMATH Keywords

elasticitysemidefinite programmingcubic symmetrypiezoelectricitypolynomial optimizationLasserre's methoddistance to a symmetry classsemialgebraic and real algebraic geometry

Mathematics Subject Classification ID

Semidefinite programming (90C22) Classical linear elasticity (74B05) Anisotropy in solid mechanics (74E10) Semialgebraic sets and related spaces (14P10) Polynomial optimization (90C23)

Cites Work

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• On anisotropic polynomial relations for the elasticity tensor
• On polynomial optimization over non-compact semi-algebraic sets
• On a conjecture of Montgomery
• The geometry of spontaneous symmetry breaking
• The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry
• Linear and nonlinear programming.
• On obtaining effective transversely isotropic elasticity tensors
• Invariant properties for finding distance in space of elasticity tensors
• Semidefinite characterization and computation of zero-dimensional real radical ideals
• Inequalities defining orbit spaces
• Finite orbit structure on locally compact manifolds
• The ellipsoid method and its consequences in combinatorial optimization
• Determination of the symmetries of an experimentally determined stiffness tensor: Application to acoustic measurements
• The description, classification, and reality of material and physical symmetries
• Symmetry classes for elasticity tensors
• Symmetry classes and harmonic decomposition for photoelasticity tensors
• Isotropic invariants of traceless symmetric tensors of orders three and four
• Symmetry classes of piezoelectric solids
• Symmetry classes in piezoelectricity from second-order symmetries
• A note on the decomposition of tensors into traceless symmetric tensors
• Global Optimization with Polynomials and the Problem of Moments
• Distinguished representations of strictly positive polynomials
• Isotropic invariants of a completely symmetric third-order tensor
• An Introduction to Polynomial and Semi-Algebraic Optimization
• An Interior-Point Method for Minimizing the Maximum Eigenvalue of a Linear Combination of Matrices
• Seminar on Transformation Groups. (AM-46)
• On obtaining effective orthotropic elasticity tensors
• GloptiPoly 3: moments, optimization and semidefinite programming
• Semidefinite optimization
• Self-Scaled Barriers and Interior-Point Methods for Convex Programming
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• A numerical feasible interior point method for linear semidefinite programs
• Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
• Solution of the truncated complex moment problem for flat data
• Semidefinite Programming
• The truncated complex $K$-moment problem
• Optimization of Polynomials on Compact Semialgebraic Sets
• GloptiPoly
• Revisiting two theorems of Curto and Fialkow on moment matrices
• Characterization of the symmetry class of an elasticity tensor using polynomial covariants
• Linear programming. Foundations and extensions

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