On hyperbolicity cones associated with elementary symmetric polynomials

DOI10.1007/s11590-007-0067-0zbMath1246.52015OpenAlexW2087191943MaRDI QIDQ941028

Yuriy Zinchenko

Publication date: 4 September 2008

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-007-0067-0

zbMATH Keywords

elementary symmetric polynomialshyperbolic polynomialshyperbolicity conespositive semi-definite representability

Mathematics Subject Classification ID

Convex programming (90C25) Inequalities and extremum problems involving convexity in convex geometry (52A40)

Related Items (6)

Hyperbolic Relaxation of $k$-Locally Positive Semidefinite Matrices ⋮ Automorphisms of Rank-One Generated Hyperbolicity Cones and Their Derivative Relaxations ⋮ Hyperbolicity cones of elementary symmetric polynomials are spectrahedral ⋮ A spectrahedral representation of the first derivative relaxation of the positive semidefinite cone ⋮ Polynomial-sized semidefinite representations of derivative relaxations of spectrahedral cones ⋮ Spectrahedrality of hyperbolicity cones of multivariate matching polynomials

Cites Work

• On Nesterov's approach to semi-infinite programming
• Classical complexity and quantum entanglement
• Hyperbolic programs, and their derivative relaxations
• Hyperbolic Polynomials and Convex Analysis
• A Mathematical View of Interior-Point Methods in Convex Optimization
• Lectures on Modern Convex Optimization
• Linear matrix inequality representation of sets
• Hyperbolic Polynomials and Interior Point Methods for Convex Programming
• Relating Homogeneous Cones and Positive Definite Cones via T-Algebras
• The Lax conjecture is true
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