v2010.10.26 - Convex Optimization

826 INDEXhull, 62, 65, 72open, 41entry, 37, 220, 769, 774–776, 781largest, 231smallest, 231epigraph, 219, 222, 241, 242, 265, 271form, 248, 580, 581intersection, 241, 268, 272equalityconstraint, 174, 208affine, 274EDM, 535normal equation, 702errata, 212, 238, 315, 442, 660, 743Euclideanball, 39, 227, 228, 413, 703, 744smallest, 64distance, 396, 402geometry, 22, 418, 425, 729matrix, see EDMmetric, 397, 451fifth property, 397, 400, 401, 486,489, 495norm, see 2-normprojection, 136space, 36, 396, 778exclusivemutually, 172expansion, 191, 780biorthogonal, 153, 168, 186, 190, 705EDM, 510projection, 716unique, 188, 190, 193, 511, 638, 717implied by diagonalization, 188orthogonal, 58, 156, 189, 711, 713w.r.t orthant, 190exponential, 697exposed, 92closed, 511direction, 111extreme, 94, 103, 146face, 93, 147point, 93, 94, 111density, 95extreme, 92boundary, 111direction, 89, 107, 112, 144distinct, 109dual cone, 143, 186, 191, 193, 196,210–212EDM cone, 111, 510, 535one-dimensional, 109, 111origin, 109orthant, 89pointed cone, 103, 109, 151, 160PSD cone, 109, 115, 127shared, 212supporting hyperplane, 186unique, 109exposed, 94, 103, 146point, 69, 92, 94, 95, 283cone, 103, 139Fantope, 309hypercube slice, 336ray, 107, 514− F −, 95face, 42, 92affine, 95algebra, 95cone, see coneexposed, see exposedintersection, 178isomorphic, 122, 410, 509of face, 95polyhedron, 147recognition, 25smallest, 95, 122–126, 178, 179, seeconetransitivity, 95facet, 93, 186, 213factorizationmatrix, 655nonnegative matrix, 314Fan, 65, 276, 603, 658Fantope, 65, 66, 128, 246, 309extreme point, 309Farkas’ lemma, 168, 171positive definite, 286not, 287