v2010.10.26 - Convex Optimization

INDEX 829point, 39, 62positive semidefinite cone, 62unique, 61conic, 63, 70, 150empty set, 72convex, 61, 63, 64, 150, 396cone, 164dyads, 67empty set, 65extreme directions, 110orthogonal matrices, 70orthonormal matrices, 70outer product, 65permutation matrices, 69positive semidefinite cone, 127projection matrices, 65rank one matrices, 67, 68rank one symmetric matrices, 127unique, 64hyperboloid, 630hyperbox, 83, 744hypercube, 52, 83, 227, 744nonnegative, 297slice, nonnegative, 336, 383hyperdimensional, 674hyperdisc, 681hyperplane, 72, 73, 75–77, 253hypersphere radius, 75independence, 86intersection, 86, 178convex set, 80, 523movement, 75, 89, 90, 230normal, 76separating, 84, 165, 170, 171strictly, 84supporting, 79, 81, 82, 204, 257–259cone, 156, 158, 178, 186cone, EDM, 529cone, PSD, 121, 123exposed face, 93polarity, 82strictly, 82, 102, 103, 257, 258trivially, 79, 179unique, 257, 258vertex-description, 77hypersphere, 65, 75, 408, 413, 461circumhypersphere, 449hypograph, 243, 271, 692− I −, 782idempotent, see matrixiff, 784image, 47inverse, 47–49, 183cone, 117, 118, 164, 184magnetic resonance, 373in, 777independenceaffine, 71, 78, 142, 145preservation, 79conic, 27, 71, 140–146, 298versus dimension, 141dual cone, 196extreme direction, 144preservation, 142unique, 141, 146, 192, 194linear, 37, 71, 141, 142, 145, 298, 348,637matrix, 603of affine, 86, 88preservation, 37subspace, 37, 772inequalityangle, 400, 489matrix, 433Bessel, 711Cauchy-Schwarz, 88, 753constraint, 206, 307determinant, 607diagonal, 607eigenvalue, 603, 664generalized, 105, 153, 168dual, 168dual PSD, 180partial order, 103, 105, 116Hardy-Littlewood-Pólya, 560Jensen, 256linear, 35, 72, 169matrix, 182–184, 284, 287log, 692