v2010.10.26 - Convex Optimization

840 INDEXon cardinality k , 744on complement, 708, 740on cone, 738, 740, 745dual, 96, 156, 740EDM, 566, 567, 578, 583, 584Lorentz (second-order), 745monotone nonnegative, 474, 484,560–562, 745polyhedral, 745simplicial, 745truncated, 742on cone, PSD, 136, 555, 557, 558, 744cardinality constrained, 369geometric center subspace, 534rank constrained, 251, 558, 564, 657rank one, 369on convex set, 174, 733–735in affine subset, 745in subspace, 745, 746on convex sets, 750on dyad, 722, 725on ellipsoid, 353on Euclidean ball, 744on function domain, 243on geometric center subspace, 534, 731on halfspace, 721on hyperbox, 744on hypercube, 744on hyperplane, 719, 721, see projection,on affineon hypersphere, 744on intersection, 745on matricesrank constrained, 745on matrix, 722, 724on origin, 739, 745on orthant, 561, 741, 744in subspace, 561on range, 702on rowspace, 55on simplex, 745on slab, 721on spectral norm ball, 745on subspace, 50, 710Cartesian, 744elementary, 718hollow symmetric, 556, 743matrix, 729orthogonal complement, 96, 156, 739polyhedron, 147symmetric matrices, 743on vectorcardinality k , 744nonorthogonal, 722orthogonal, 724one-dimensional, 724order of, 548, 550, 745orthogonal, 702, 709, 724eigenvalue coefficients, 726semidefiniteness test as, 727range/rowspace, 733spectral, 527, 559, 562norm, 565, 745unique, 562successive, 750two sided, 729, 731, 733umbral, 50unique, 707, 710, 730, 733–735vectorization, 517, 731projectorbiorthogonal, 713characteristic, 704, 707, 708, 711, 712commutative, 748non, 534, 745, 749complement, 709convexity, 707, 712, 733, 735direction, 709, 713, 724nonorthogonal, 706, 707, 722dyad, 635, 704, 722Kronecker, 749linear operator, 55, 707, 712, 715, 735nonorthogonal, 406, 707, 714, 722orthogonal, 710orthonormal, 713product, 534, 723, 748range, 710semidefinite, 610, 711prototypicalcomplementarity problem, 207compressed sensing, 347