Intrinsic volumes of symmetric cones and applications in convex programming

DOI10.1007/s10107-013-0740-2zbMath1311.90092OpenAlexW1983481603MaRDI QIDQ2515035

Peter Bürgisser, Dennis Amelunxen

Publication date: 9 February 2015

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

Full work available at URL: https://doi.org/10.1007/s10107-013-0740-2

zbMATH Keywords

semidefinite programmingsymmetric conesintrinsic volumesrandom convex programsMehta's integral

Mathematics Subject Classification ID

Semidefinite programming (90C22) Spherical and hyperbolic convexity (52A55)

Related Items

Conic support measures, Random conical tessellations, A Lower Bound on the Positive Semidefinite Rank of Convex Bodies, Conic intrinsic volumes of Weyl chambers, Intrinsic volumes of polyhedral cones: a combinatorial perspective, Sharp recovery bounds for convex demixing, with applications, Random positive operator valued measures, Intersection probabilities and kinematic formulas for polyhedral cones, Intrinsic volumes of symmetric cones and applications in convex programming, Faces in random great hypersphere tessellations, From Steiner formulas for cones to concentration of intrinsic volumes, Symmetry Adapted Gram Spectrahedra, Probabilistic analysis of the Grassmann condition number, Sensitivity of low-rank matrix recovery, Generic Spectrahedral Shadows, A new approach to weak convergence of random cones and polytopes

Cites Work

• The algebraic degree of semidefinite programming
• Curvature measures and Steiner formulae in space forms
• Complementarity and nondegeneracy in semidefinite programming
• Euclidean Jordan algebras and interior-point algorithms
• Solving linear programs with finite precision. I: Condition numbers and random programs
• Self-scaled barrier functions on symmetric cones and their classification
• Probabilistic analysis of the Grassmann condition number
• Intrinsic volumes of symmetric cones and applications in convex programming
• Über die Steinersche Formel für Parallelflächen
• A Mathematical View of Interior-Point Methods in Convex Optimization
• Lectures on Modern Convex Optimization
• Smooth analysis of the condition number and the least singular value
• Stochastic and Integral Geometry
• The importance of the Selberg integral
• A general formula for the algebraic degree in semidefinite programming
• Smallest singular value of a random rectangular matrix
• A Problem in Geometric Probability.
• Random polytopes: Their definition, generation and aggregate properties
• The kinematic formula in Riemannian homogeneous spaces
• Barrier Functions in Interior Point Methods
• Self-Scaled Barriers and Interior-Point Methods for Convex Programming
• Primal-Dual Interior-Point Methods for Self-Scaled Cones
• Random Fields and Geometry
• Steiner’s formulae on a general 𝑆ⁿ⁺¹
• On Parallel Hypersurfaces in the Elliptic and Hyperbolic n-Dimensional Space
• Quaternions and matrices of quaternions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item