Generic Spectrahedral Shadows

DOI10.1137/140978478zbMath1346.14132arXiv1407.5219OpenAlexW2962767810MaRDI QIDQ5259828

Bernd Sturmfels, Rainer Sinn

Publication date: 29 June 2015

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

Full work available at URL: https://arxiv.org/abs/1407.5219

zbMATH Keywords

extended formulationsalgebraic boundary, algebraic degree of semidefinite programmingspectahedral shadows

Mathematics Subject Classification ID

Semidefinite programming (90C22) Semialgebraic sets and related spaces (14P10) Projective techniques in algebraic geometry (14N05)

Related Items

Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without \(K_{5}\) minors, A Lower Bound on the Positive Semidefinite Rank of Convex Bodies, The geometry of SDP-exactness in quadratic optimization, Semidefinite Representation for Convex Hulls of Real Algebraic Curves, Positive semidefinite rank and nested spectrahedra, Bad projections of the PSD cone, Operator systems and convex sets with many normal cones, Exact Algorithms for Linear Matrix Inequalities, Exact Duality in Semidefinite Programming Based on Elementary Reformulations

Uses Software

• Macaulay2

Cites Work

• Algebraic boundaries of convex semi-algebraic sets
• Semidefinite representation of convex sets
• The algebraic degree of semidefinite programming
• Some geometric results in semidefinite programming
• Quartic spectrahedra
• Intrinsic volumes of symmetric cones and applications in convex programming
• Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
• Chapter 5: Dualities
• A general formula for the algebraic degree in semidefinite programming
• Semidefinite Optimization and Convex Algebraic Geometry
• Unnamed Item