A Note on the Convex Hull of Finitely Many Projections of Spectrahedra

2009/08/24 by Tim Netzer, Netzer, Tim, Rainer Sinn +1 · 3 citations
Engineering · Mathematics · #14P10 #15A48 #90C22 #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Optimization and Control (math.OC) #Point processes and geometric inequalities #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.0908.3386

openalex publication_date 2009/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A spectrahedron is a set defined by a linear matrix inequality. A projection of a spectrahedron is often called a semidefinitely representable set. We show that the convex hull of a finite union of such projections is again a projection of a spectrahedron. This improves upon the result of Helton and Nie, who prove the same result in the case of bounded sets.

Cited by

• Conic programming: infeasibility certificates and projective geometry
• Smooth Hyperbolicity Cones are Spectrahedral Shadows
• Positive Polynomials and Projections of Spectrahedra

Related

• Containment Problems for Projections of Polyhedra and Spectrahedra
• Spectrahedra and Convex Hulls of Rank-One Elements
• Exposed faces of semidefinitely representable sets
• Positive Polynomials and Projections of Spectrahedra
• Deciding polyhedrality of spectrahedra