2018/05/24 by Javier Peña, Javier Pena, Pena, Javier +2
Decision Sciences · Engineering · Mathematics · #65F22 #65K10 #90C25 #Advanced Optimization Algorithms Research #Combinatorics #Computer science #Conic section #FOS: Mathematics #Geometry #Grassmannian #Homogeneous #Mathematical optimization #Mathematics #Measure (data warehouse) #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Sparse and Compressive Sensing Techniques #Symmetry (geometry) #math.OC #msc:65F22 #msc:65K10 #msc:90C25
paper · pdf · doi:10.48550/arxiv.1805.09494
published in arXiv (Cornell University) (Cornell University) · 25 pages, 2 figures. arXiv admin note: text overlap with arXiv:1604.04637
openalex publication_date 2018/05/24 · arxiv created 2020/01/23 · arxiv updated 2020/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We offer a unified treatment of distinct measures of well-posedness for homogeneous conic systems. To that end, we introduce a distance to infeasibility based entirely on geometric considerations of the elements defining the conic system. Our approach sheds new light on and connects several well-known condition measures for conic systems, including \em Renegar's distance to infeasibility, the \em Grassmannian condition measure, a measure of the \em most interior solution, and other geometric measures of \em symmetry and of \em depth of the conic system.