v2010.10.26 - Convex Optimization

INDEX 845faces, 106intersection, 102conic coordinates, 213convexity condition, 256decompositiondyad, 631directional derivative, 681discretized membership, 176dual cone intersection, 209duality, weak, 288EDM, 461eigenvalueof difference, 608of sum, 608order, 607zero, 626elliptope vertices, 461exposed, 111extreme existence, 92extremes, 110Farkas’ lemma, 168, 171not positive definite, 287positive definite, 286positive semidefinite, 284fundamentalalgebra, 617algebra, linear, 85convex optimization, 274generalized inequality and membership,168Geršgorin discs, 132gradient monotonicity, 255Hahn-Banach, 74, 79, 84halfspaces, 74Hardy-Littlewood-Pólya, 560hypersphere, 461inequalities, 560intersection, 46inverse image, 47, 51closedness, 183Klee, 110line, 266, 272linearly independent dyads, 637majorization, 595mean value, 686Minkowski, 148monotone nonnegative sort, 561Moreau decomposition, 206, 740Motzkin, 734transposition, 173nonexpansivity, 743pointed cones, 103positive semidefinite, 600cone subsets, 136matrix sum, 135principal submatrix, 609symmetric, 610projectionalgebraic complement, 741minimum-distance, 734, 735on affine, 715on cone, 738on convex set, 734, 735on PSD geometric intersection, 534on subspace, 50via dual cone, 741via normal cone, 735projectorrank/trace, 712semidefinite, 610proper-cone boundary, 106Pythagorean, 360, 431, 747range of dyad sum, 638rankaffine dimension, 449partitioned matrix, 614Schur-form, 614, 615trace, 708real eigenvector, 617sparse sampling, 339, 372sparsity, 229Tour, 465Weyl, 148eigenvalue, 608tight, 399, 782trace, 238, 591, 592, 654, 656, 693tr , 606, 784/rank gap, 571eigenvalues, 602heuristic, 310–312, 384, 570–573, 655