v2010.10.26 - Convex Optimization

INDEX 821circular, 130construction, 508convexity, 502decomposition, 538dual, 529, 530, 535, 540, 542–544extreme direction, 510face, 509, 511interior, 499, 507one-dimensional, 111positive semidefinite, 511, 519, 535projection, 566, 578, 581empty set, 100face, 106intersection, 178pointed, 103PSD, 147PSD, smallest, 122–126, 518, 531,541smallest, 102, 139, 178, 179, 230, 281,350, 509facet, 186, 213halfline, 96, 101, 103, 109, 111, 142, 151halfspace, 151, 160hull, 164ice cream, see cone, circularinterior, see interiorintersection, 102, 164pointed, 103invariance, see invarianceLorentzcircular, 101, 129dual, 165, 182polyhedral, 149, 165majorization, 595membership, see membership relationmonotone, 199–201, 472, 586, 667nonnegative, 197–199, 474, 475, 481,483, 484, 560–562, 586, 595, 745negative, 187, 717nonconvex, 97–100normal, 203, 204, 206, 224, 516, 735,741, 763–766affine, 765elliptope, 764membership relation, 203orthant, 203one-dimensional, 96, 101, 103, 142, 151EDM, 111PSD, 109origin, 72, 100, 102, 103, 107, 109, 142orthant, see orthantorthogonal complement, 166, 740, 765pointed, 102, 103, 106–109, 151, 168,188, 201closed convex, 103, 144dual, 151, 163extreme, 103, 109, 151, 160face, 103polyhedral, 108, 151, 184, 185polar, 96, 156, 516, 739, 780polyhedral, 70, 142, 148–151, 160dual, 143, 165, 170, 176, 181, 184,186equilateral, 181facet, 186, 213halfspace-description, 148majorization, 586pointed, 108, 151, 184, 185proper, 143vertex-description, 70, 150, 170, 185positive semidefinite, 43, 113–116, 533boundary, 114, 119, 135, 287, 519circular, 129–132, 235dimension, 122dual, 180EDM, 535extreme direction, 109, 115, 127face, 147face, smallest, 122–126, 518, 531, 541hyperplane, supporting, 121, 123inscription, 133interior, 114, 286inverse image, 117, 118one-dimensional, 109optimization, 282polyhedral, 132rank, 122–126, 136, 279visualization, 280productCartesian, 102, 103, 163