v2010.10.26 - Convex Optimization

836 INDEXhyperplane, 73injective, 53intersection, 88orthogonal complement, 85product, 604, 634, 638, 710pseudoinverse, 699, 700set, 178sum, 90vectorized, 92− O − , 782objective, 83, 781convex, 274strictly, 567, 573function, 83, 84, 162, 173, 203, 205, 781linear, 238, 325, 419multidimensional, 104, 105, 222, 223,332, 380nonlinear, 240polynomial, 360quadratic, 248nonconvex, 668real, 222value, 288, 304unique, 275offset, see invariance, translationon, 777one-to-one, 777, see injectiveonly if, 773onto, 777, see surjectiveopen, see setoperator, 782adjoint, 50, 51, 164, 537, 769, 776self, 409, 536, 591affine, see functioninjective, see injectiveinvertible, 49, 53, 55, 183linear, 47, 59, 220, 237, 238, 405, 441,443, 485, 512, 591, 732projector, 707, 712, 715, 735nonlinear, 220, 240nullspace, 435, 439, 441, 443, 732permutation, 231, 334, 559, 563, 585,775projection, see projectorsurjective, see surjectiveunitary, 54optimalitycondition, 289directional derivative, 681dual, 160first order, 173, 174, 203–208KKT, 206, 208, 557, 668semidefinite program, 290Slater, 162, 216, 285, 289, 290unconstrained, 174, 251, 252, 730constraintconic, 205, 206, 208equality, 174, 208inequality, 206nonnegative, 206global, 8, 222, 247, 274perturbation, 304optimization, 21, 273algebra, 653, 654combinatorial, 69, 83, 230, 292, 356,362, 365, 461, 588conic, see problemconvex, 7, 21, 222, 274, 417art, 8, 298, 318, 589fundamental, 274invariance, 239, 654multiobjective, 104, 105, 222–224, 332,380tractable, 274vector, 104, 105, 222–224, 332, 380ordernatural, 50, 591, 781nonincreasing, 561, 620, 621, 775of projection, 548partial, 64, 101, 103–105, 116, 177, 186,187, 606, 782, 785generalized inequality, 103, 105, 116orthant, 177property, 103, 105total, 103, 104, 156, 783transitivity, 103, 116, 606origin, 36cone, 72, 100, 102, 103, 107, 109, 142projection of, 227, 228, 703, 719