LMI approximations for the radius of the intersection of ellipsoids: Survey.

DOI10.1023/A:1026454804250zbMath1033.93058OpenAlexW1505246359MaRDI QIDQ5929424

Denis Arzelier, Didier Henrion, Sophie Tarbouriech

Publication date: 4 April 2001

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1026454804250

zbMATH Keywords

nonconvex optimizationconvex relaxationsellipsoidslinear matrix inequality relaxationmaximum norm vectorrobust control synthesis

Mathematics Subject Classification ID

Related Items (12)

On Local Minimizers of Nonconvex Homogeneous Quadratically Constrained Quadratic Optimization with at Most Two Constraints ⋮ Ellipsoidal bounds for uncertain linear equations and dynamical systems ⋮ Multi-model predictive control based on LMI: from the adaptation of the state-space model to the analytic description of the control law ⋮ Comment on: ``Approximation algorithms for quadratic programming ⋮ Data assimilation and sampling in Banach spaces ⋮ A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints ⋮ Global optimization in Hilbert space ⋮ On equivalence of major relaxation methods for minimum ellipsoid covering intersection of ellipsoids ⋮ Direct data-driven recursive controller unfalsification with analytic update ⋮ Chebyshev center of the intersection of balls: complexity, relaxation and approximation ⋮ Improved semidefinite approximation bounds for nonconvex nonhomogeneous quadratic optimization with ellipsoid constraints ⋮ Semidefinite approximation bound for a class of nonhomogeneous nonconvex quadratically constrained quadratic programming problem

Uses Software

• LMI toolbox

Cites Work

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• Method of centers for minimizing generalized eigenvalues
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• Approximation algorithms for quadratic programming
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• Hidden convexity in some nonconvex quadratically constrained quadratic programming
• On maximization of quadratic form over intersection of ellipsoids with common center
• Robust Convex Optimization
• Linear Matrix Inequalities in System and Control Theory
• Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
• NP-Hardness of Some Linear Control Design Problems
• Determinant Maximization with Linear Matrix Inequality Constraints
• Semidefinite relaxation and nonconvex quadratic optimization
• Copositive realxation for genera quadratic programming
• Semidefinite Programming
• State bounding with ellipsoidal set description of the uncertainty

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