Empirical Properties of Optima in Free Semidefinite Programs

DOI10.1080/10586458.2021.1980457zbMath1522.90077arXiv2006.02248OpenAlexW3210289813MaRDI QIDQ6050736

Yi Fu, J. William Helton, Eric Evert, Unnamed Author

Publication date: 19 September 2023

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.02248

zbMATH Keywords

extreme pointlinear matrix inequalityspectrahedronmatrix convex setArveson boundaryfree semidefinite programming

Mathematics Subject Classification ID

Semidefinite programming (90C22) Linear inequalities of matrices (15A39) Convex sets and cones of operators (47L07)

Cites Work

• Unnamed Item
• Unnamed Item
• Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets
• Every convex free basic semi-algebraic set has an LMI representation
• Free probability and random matrices
• Pure matrix states on operator systems
• The Choquet boundary of an operator system
• Extreme points of matrix convex sets, free spectrahedra, and dilation theory
• Matrix convex sets without absolute extreme points
• Minimal and maximal matrix convex sets
• Compressions of compact tuples
• Some geometric results in semidefinite programming
• The matricial relaxation of a linear matrix inequality
• An introduction to matrix convex sets and free spectrahedra
• Dilation theory in finite dimensions and matrix convexity
• Arveson extreme points span free spectrahedra
• Subalgebras of \(C^ *\)-algebras
• Optimization of Polynomials in Non-Commuting Variables
• Foundations of Free Noncommutative Function Theory
• The noncommutative Choquet boundary
• The Krein-Milman theorem in operator convexity
• Extremal Matrix States on Operator Systems
• Convex Matrix Inequalities Versus Linear Matrix Inequalities
• Strongly Peaking Representations and Compressions of Operator Systems
• Free convex sets defined by rational expressions have LMI representations
• Boundary representations and pure completely positive maps
• Spectrahedral Containment and Operator Systems with Finite-Dimensional Realization

This page was built for publication: Empirical Properties of Optima in Free Semidefinite Programs