v2010.10.26 - Convex Optimization

INDEX 819bees, 30, 413Bellman, 276bijective, 50, 53, 56, 119, 185Gram form, 439, 442inner-product form, 443, 444invertible, 53, 700isometry, 54, 485linear, 52, 54, 57, 60, 144orthogonal, 54, 485, 563, 647, 665biorthogonaldecomposition, 704, 713expansion, 153, 168, 186, 190, 705EDM, 510projection, 716unique, 188, 190, 193, 511, 638, 717biorthogonality, 188, 191condition, 186, 619, 638Birkhoff, 69Boolean, see problemboundlower, 552polyhedral, 501boundary, 39, 40, 46, 64, 96-point, 94extreme, 111of affine, 38, 46of cone, 106, 178, 183, 185EDM, 499, 507, 514membership, 169, 178, 185, 287PSD, 40, 114, 119, 135–138, 287, 519ray, 107of halfspace, 72of hypercube slice, 383of open set, 41of point, 46of ray, 96relative, 39, 40, 46, 64, 96bounded, 64, 84bowl, 680, 681box, 83, 744bridge, 429, 458, 527, 553, 569Bunt, 137, 734calculus− C −, 36matrix, 669of inequalities, 7of variations, 173Carathéodory’s theorem, 168, 726cardinality, 333, 402, 784, 7861-norm heuristic, 335, 336, 572-one, 227, 347constraint, see constraintconvex envelope, see convexgeometry, 227, 230, 347minimization, 227, 228, 333, 340,351–353, 380Boolean, 292nonnegative, 229, 230, 233, 333, 337,339, 346–350rank connection, 310rank one, 369rank, full, 298quasiconcavity, 233, 334regularization, 345, 370Cartesianaxes, 38, 63, 80, 99, 108, 154, 166, 336,744cone, see orthantcoordinates, 480product, 47, 284, 756, 778cone, 102, 103, 163function, 224subspace, 336, 744Cauchy-Schwarz, 88, 753Cayley-Mengerdeterminant, 491, 493form, 449, 470, 471, 559, 584cellular, 426telephone network, 425centergeometric, 407, 411, 435, 478gravity, 435mass, 435central path, 283certificate, 217, 287, 288, 309, 391null, 170, 179chain rule, 676two argument, 676Chu, 7