Limitations on the Expressive Power of Convex Cones without Long Chains of Faces

DOI10.1137/19M1245670zbMath1436.90108arXiv1902.06401OpenAlexW3014980195MaRDI QIDQ5222131

James Saunderson

Publication date: 1 April 2020

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.06401

zbMATH Keywords

liftsconic optimizationhyperbolicity conecone factorization

Mathematics Subject Classification ID

Convex programming (90C25)

Related Items (6)

Lifting for Simplicity: Concise Descriptions of Convex Sets ⋮ Hyperbolic secant varieties of \(M\)-curves ⋮ Automorphisms of Rank-One Generated Hyperbolicity Cones and Their Derivative Relaxations ⋮ On eigenvalues of symmetric matrices with PSD principal submatrices ⋮ Fitting tractable convex sets to support function evaluations ⋮ Second-Order Cone Representation for Convex Sets in the Plane

Uses Software

• SPOTless

Cites Work

• Unnamed Item
• Amoebas, nonnegative polynomials and sums of squares supported on circuits
• Facial reduction algorithms for conic optimization problems
• Non-representable hyperbolic matroids
• Positive definite completions of partial Hermitian matrices
• The algebraic degree of semidefinite programming
• Neighborly embedded manifolds
• Positive semidefinite matrices with a given sparsity pattern
• Perfect cones
• Exact duals and short certificates of infeasibility and weak infeasibility in conic linear programming
• Cones of diagonally dominant matrices
• A bound on the Carathéodory number
• On representing the positive semidefinite cone using the second-order cone
• Hyperbolic programs, and their derivative relaxations
• The lattice of faces of a finite dimensional cone
• Lectures on Modern Convex Optimization
• Relative Entropy Relaxations for Signomial Optimization
• A Lower Bound on the Positive Semidefinite Rank of Convex Bodies
• Lifts of Convex Sets and Cone Factorizations
• Do Sums of Squares Dream of Free Resolutions?
• DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
• A Note on Hyperbolic Polynomials.
• Optimal Size of Linear Matrix Inequalities in Semidefinite Approaches to Polynomial Optimization
• Strong Duality in Conic Linear Programming: Facial Reduction and Extended Duals

This page was built for publication: Limitations on the Expressive Power of Convex Cones without Long Chains of Faces