v2010.10.26 - Convex Optimization

838 INDEXnonnegative, 229, 230, 335, 336, 339,346–350, 572Boolean, 69, 83, 292, 362, 461cardinality, see cardinalitycombinatorial, 69, 83, 230, 292, 356,362, 365, 461, 588complementarity, 206linear, 207completion, 319–322, 330, 376, 398,399, 418, 421, 422, 457, 464, 465,494, 495, 522–524, 589geometry, 522semidefinite, 759, 760compressed sensing, see compressedconcave, 274conic, 162, 205, 206, 208, 224, 275dual, 162, 275convex, 162, 174, 205, 208, 226, 238,247, 249, 278, 284, 564, 733definition, 274geometry, 21, 27nonlinear, 273statement as solution, 7, 273tractable, 274dual, see dualepigraph form, 248, 580, 581equivalent, 309, 781feasibility, 141, 151, 178, 179, 783semidefinite, 288, 308, 309, 390fractional, inverted, see functionmax cut, 365minimax, 64, 160, 162nonlinear, 417convex, 273open, 30, 135, 313, 475, 511, 588primal, see primalProcrustes, see Procrustesproximity, 547, 549, 552, 555, 566, 578EDM, nonconvex, 562in spectral norm, 565rank heuristic, 572, 575SDP, Gram form, 569semidefinite program, 558, 568, 579quadraticnonconvex, 668rank, see ranksame, 781stress, 262, 554, 576tractable, 274procedurerank reduction, 300Procrustescombinatorial, 356compressed sensing, 359diagonal, 667linear program, 665maximization, 664orthogonal, 661two sided, 663, 666orthonormal, 355symmetric, 666translation, 662unique solution, 662product, 271, 675Cartesian, 47, 284, 756, 778cone, 102, 103, 163function, 224commutative, 268, 291, 603–605, 629,748determinant, 604direct, 674eigenvalue, 603, 605, 606, 661matrix, 605, 606fractional, see functionfunction, see functiongradient, 673Hadamard, 51, 566, 592, 593, 676, 772positive semidefinite, 606innermatrix, 405vector, 50, 271, 276, 372, 431, 723,774vectorized matrix, 50, 601Kronecker, 118, 592–594, 665, 674, 675,692eigen, 594inverse, 376orthogonal, 651positive semidefinite, 402, 606projector, 749