v2010.10.26 - Convex Optimization

844 INDEXnorm, 70, 268, 552, 565, 624, 634, 641,642, 654, 745, 786ball, 70, 745dual, 655, 786inequality, 70, 786Schur-form, 268, 654projection, see projectionsphere packing, 413steepest descent, 251, 680strictcomplementarity, 291feasibility, 285, 289positivity, 451triangle inequality, 454Sturm, 631subject to, 783submatrixprincipal, 124, 417, 487, 492, 509, 609leading, 124, 452, 454subspace, 36algebra, 36, 85, 86, 634antihollow, 59antisymmetric, 59, 60, 549antisymmetric, 56Cartesian, 336, 744complementary, see complementfundamental, 49, 85, 86, 635, 639, 640,700, 710geometric center, 439, 440, 498, 529,532–534, 570, 629, 731orthogonal complement, 121, 435,529, 731hollow, 58, 440, 533intersection, 88hyperplane, 86nullspace basis span, 87proper, 36representation, 85symmetric hollow, 58tangent, 121translation invariant, 435, 441, 529, 731vectorized, 90, 92successiveapproximation, 750projection, 750sum, 46of eigenvalues, 53, 602of functions, 224, 255, 272of matriceseigenvalues, 608nullspace, 90rank, 135, 603of singular values, 53, 67, 654, 655vector, 46, 637, 772orthogonal, 773unique, 56, 156, 637, 772, 773supremum, 64, 272, 653–656, 783of affine functions, 241, 655of convex functions, 268, 272surjective, 54, 439, 441, 443, 560, 777linear, 443, 444, 461, 463svec, 57, 275, 785Swiss roll, 26symmetry, 397− T −, 769tangentline, 43, 419subspace, 121tangential, 43, 82, 420Taylor series, 679, 685–687tensor, 672–675tesseract, 52tetrahedron, 151–153, 346, 491angle inequality, 489regular, 489, 502Theobald, 603theorem0 eigenvalues, 626alternating projectiondistance, 753alternative, 170–173, 179EDM, 544semidefinite, 287weak, 172Barvinok, 139Bunt-Motzkin, 734Carathéodory, 168, 726compressed sensing, 339, 372cone