v2007.09.17 - Convex Optimization

16 LIST OF FIGURES92 Largest ten eigenvalues of −VN TOV N . . . . . . . . . . . . . . 37493 Relative-angle inequality tetrahedron . . . . . . . . . . . . . . 38194 Nonsimplicial pyramid in R 3 . . . . . . . . . . . . . . . . . . . 3856 EDM cone 38995 Relative boundary of cone of Euclidean distance matrices . . . 39296 Intersection of EDM cone with hyperplane . . . . . . . . . . . 39497 Neighborhood graph . . . . . . . . . . . . . . . . . . . . . . . 39698 Trefoil knot untied . . . . . . . . . . . . . . . . . . . . . . . . 39999 Trefoil ribbon . . . . . . . . . . . . . . . . . . . . . . . . . . . 401100 Example of V X selection to make an EDM . . . . . . . . . . . 404101 Vector V X spirals . . . . . . . . . . . . . . . . . . . . . . . . . 406102 Three views of translated negated elliptope . . . . . . . . . . . 414103 Halfline T on PSD cone boundary . . . . . . . . . . . . . . . . 418104 Vectorization and projection interpretation example . . . . . . 419105 Orthogonal complement of geometric center subspace . . . . . 424106 EDM cone construction by flipping PSD cone . . . . . . . . . 425107 Decomposing a member of polar EDM cone . . . . . . . . . . 430108 Ordinary dual EDM cone projected on S 3 h . . . . . . . . . . . 4367 Proximity problems 439109 Pseudo-Venn diagram . . . . . . . . . . . . . . . . . . . . . . 442110 Elbow placed in path of projection . . . . . . . . . . . . . . . 443111 Convex envelope . . . . . . . . . . . . . . . . . . . . . . . . . 463A Linear algebra 481112 Geometrical interpretation of full SVD . . . . . . . . . . . . . 510B Simple matrices 519113 Four fundamental subspaces of any dyad . . . . . . . . . . . . 521114 Four fundamental subspaces of a doublet . . . . . . . . . . . . 525115 Four fundamental subspaces of elementary matrix . . . . . . . 526116 Gimbal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534