v2010.10.26 - Convex Optimization

INDEX 843nonconvex, 40, 97–101nullspace, 178open, 36, 38–41, 169and closed, 36, 41orthogonal, 178projection of, 50Schur-form, 117smooth, 459solution, 222, 781sublevel, 204, 242, 251, 258, 265, 270convex, 243, 259, 612quasiconvex, 270sum, 46, 772superlevel, 243, 270union, 46, 96, 98, 100, 125Shannon, 372shape, 23Sherman-Morrison, 636shift, see invariance, translationshroud, 437, 438, 515cone, 181, 543SIAM, 274signaldropout, 341processingdigital, 341, 372, 385, 476simplex, 151–153area, 491content, 493method, 332, 414nonnegative, 346, 347regular, 492unit, 151, 152volume, 493singular value, 621, 654σ , 592, 775decomposition, 620–625, 655compact, 620diagonal, 668full, 622geometrical, 623pseudoinverse, 624subcompact, 621symmetric, 625, 667eigenvalue, 621, 624, 625inequality, 70, 666inverse, 624largest, 70, 268, 654, 745, 786normal matrix, 53, 621sum of, 53, 67, 654, 655symmetric matrix, 624, 625triangle inequality, 67skinny, 191, 769slab, 38, 324, 721slackcomplementary, 290variable, 275, 284, 307Slater, 162, 216, 285, 289, 290slice, 129, 182, 425, 680, 681slope, 251solid, 147, 152, 489solutionanalytical, 248, 273, 653feasible, 83, 173, 285, 751–755, 781dual, 289, 290strictly, 285, 289numerical, 330optimal, 83, 88–90, 222, 781problem statement as, 7, 273set, 222, 781trivial, 37unique, 45, 221, 222, 419, 420, 565, 567,573, 583vertex, 83, 230, 359, 414sortfunction, 231, 334, 559, 563, 585, 775index matrix, 481largest entries, 231monotone nonnegative, 561smallest entries, 231span, 63, 777sparsity, 225, 227–230, 233, 292, 298, 333,334, 337–340, 351–353, 369, 372gradient, 373nonnegative, 229, 339, 346–350spectralcone, 470, 472, 559dual, 475orthant, 562inequality, 70, 470