On the bilinearity rank of a proper cone and Lyapunov-like transformations

DOI10.1007/s10107-013-0715-3zbMath1302.90224OpenAlexW2102229945MaRDI QIDQ463722

Jiyuan Tao, M. Seetharama Gowda

Publication date: 17 October 2014

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-013-0715-3

zbMATH Keywords

complementaritysymmetric coneproper coneLyapunov-like transformationbilinearity rankcompletely positive coneprimal-dual linear program

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Finite-dimensional structures of Jordan algebras (17C55) Convex sets and cones of operators (47L07)

Related Items (14)

The monotone extended second-order cone and mixed complementarity problems ⋮ Unnamed Item ⋮ The \(p\)-cones in dimension \(n\geq 3\) are not homogeneous when \(p\neq 2\) ⋮ Some characterizations of cone preserving \(Z\)-transformations ⋮ Automorphisms of Rank-One Generated Hyperbolicity Cones and Their Derivative Relaxations ⋮ Minimum eigenvalue inequalities for \(Z\)-transformations on proper and symmetric cones ⋮ Lyapunov rank of polyhedral positive operators ⋮ Permutation invariant proper polyhedral cones and their Lyapunov rank ⋮ How to project onto extended second order cones ⋮ The Lyapunov rank of extended second order cones ⋮ An improved bound for the Lyapunov rank of a proper cone ⋮ Unnamed Item ⋮ The Lyapunov rank of an improper cone ⋮ Tight bounds on Lyapunov rank

Cites Work

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• The automorphism group of a completely positive cone and its Lie algebra
• Positive groups on \(\mathcal H^n\) are completely positive
• Bilinear optimality constraints for the cone of positive polynomials
• Z-transformations on proper and symmetric cones
• On the \(\mathbf P\)-property of \(\mathbf Z\) and Lyapunov-like transformations on Euclidean Jordan algebras
• On Common Linear/Quadratic Lyapunov Functions for Switched Linear Systems
• A REPRESENTATION THEOREM FOR LYAPUNOV-LIKE TRANSFORMATIONS ON EUCLIDEAN JORDAN ALGEBRAS
• State Constraints in Convex Control Problems of Bolza
• Cross-Positive Matrices
• Numerical Methods for Quasi‐Linear Elliptic Equations with Nonlinear Boundary Conditions

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