v2007.09.17 - Convex Optimization

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722 INDEXnormal, 175, 415, 622, 642, 643elliptope, 644orthant, 177orthogonal, 143pointed, 86, 146, 161, 174closed convex, 87, 122polyhedral, 92, 129polar, 81, 135, 415, 620polyhedral, 59, 121, 127dual, 155, 157, 159halfspace description, 127majorization, 477pointed, 157proper, 123positive semidefinite, 97, 425boundary, 418circular, 108face, 417inscription, 112inverse image, 101optimization, 232polyhedral, 113rank, 230visualization, 229proper, 89, 179quadratic, 86recession, 138second order, 86self-dual, 154simplicial, 60, 131, 132, 160dual, 160, 167spectral, 362, 451dual, 367orthant, 454tangent, 415unique, 97, 135, 391congruence, 361congruent, 330coniccombination, 59hull, 59independence, 25, 120–122, 125preservation, 122problem, 226sectioncircular cone, 111conically independent, 120conici(), 653conservationdimension, 340, 512, 513constellation, 20constraintcardinality, 273, 285equality, 151Gram, 305inequality, 255nonconvex, 276polynomial, 276rank, 256, 276, 450sort, 376content, 385, 686contour plot, 176, 212convergence, 257, 377, 628geometric, 630convexcombination, 34, 59cone, 43, 85envelope, 245, 266, 318, 462equivalent, 267form, 225function, 183geometry, 33hull, 53, 56, 292of outer product, 57iteration, 256, 257, 273, 274, 467stall, 275, 279
INDEX 723optimization, 7, 186, 226, 311polyhedron, 56, 126halfspace description, 126vertices, 128problem, 140, 151, 177, 193, 200,228, 234, 456, 614geometry, 19, 25tractable, 226set, 34Schur-form, 100simultaneously, 198, 199, 217strictly, 185convexity, 183, 327first order, 210, 211, 214, 215second order, 213, 217coordinate, 166Crippen & Havel, 322criteriamatrix, 342cubix, 552, 555, 683curvature, 220decimate(), 658decomposition, 683biorthogonal, 585, 594dyad, 517eigen, 504orthonormal, 592, 593singular value, 507compact, 507full, 508subcompact, 508Delsarte method, 308dense, 79derivative, 204directional, 213, 551, 559, 562second, 564table, 572descriptionconversion, 134halfspace, 62dual cone, 152vertex, 59, 158of halfspace, 124determinant, 380, 491, 503, 578diagonal, 481, 538dominance, 114diagonalizable, 161, 504simultaneously, 240, 494, 515diagonalization, 39, 504expansion by, 161symmetric, 506difference, 42PSD matrices, 118vector, 43diffusion, 397dilation, 374dimension, 36affine, 21, 36, 53, 337, 339, 349,429low, 315minimization, 462, 474reduction, 386spectral projection, 475complementary, 73conservation, 340, 512, 513embedding, 54positive semidefinite cone, 105Précis, 340rank, 339, 340direction, 81, 91exposed, 94extreme, 91, 158PSD cone, 99matrix, 256disc, 59
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DattorroCONVEXOPTIMIZATION&EUCLIDEA
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Meboo Publishing USA345 Stanford Sh
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EDM = S h ∩ ( S ⊥ c − S +)
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There is a great race under way to
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10 CONVEX OPTIMIZATION & EUCLIDEAN
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12 CONVEX OPTIMIZATION & EUCLIDEAN
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14 LIST OF FIGURES24 Nonconvex cone
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16 LIST OF FIGURES92 Largest ten ei
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List of Tables2 Convex geometryTabl
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20 CHAPTER 1. OVERVIEWFigure 1: Ori
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22 CHAPTER 1. OVERVIEWFigure 3: [13
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24 CHAPTER 1. OVERVIEWFigure 5: Swi
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26 CHAPTER 1. OVERVIEWoriginalrecon
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28 CHAPTER 1. OVERVIEWFigure 8: Rob
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30 CHAPTER 1. OVERVIEWnoveltyp.120
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32 CHAPTER 1. OVERVIEW
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34 CHAPTER 2. CONVEX GEOMETRY2.1 Co
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36 CHAPTER 2. CONVEX GEOMETRY2.1.3
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38 CHAPTER 2. CONVEX GEOMETRY(a)R(b
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40 CHAPTER 2. CONVEX GEOMETRYwhere
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42 CHAPTER 2. CONVEX GEOMETRYNow le
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46 CHAPTER 2. CONVEX GEOMETRYand wh
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48 CHAPTER 2. CONVEX GEOMETRY2.2.1.
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52 CHAPTER 2. CONVEX GEOMETRYAny ma
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54 CHAPTER 2. CONVEX GEOMETRYIn par
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58 CHAPTER 2. CONVEX GEOMETRYsvec
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60 CHAPTER 2. CONVEX GEOMETRYFigure
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64 CHAPTER 2. CONVEX GEOMETRY11−1
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66 CHAPTER 2. CONVEX GEOMETRYHyperp
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68 CHAPTER 2. CONVEX GEOMETRYCH −
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70 CHAPTER 2. CONVEX GEOMETRYnonemp
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72 CHAPTER 2. CONVEX GEOMETRYto vec
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78 CHAPTER 2. CONVEX GEOMETRYABCDFi
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82 CHAPTER 2. CONVEX GEOMETRYX(a)00
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84 CHAPTER 2. CONVEX GEOMETRYXXFigu
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86 CHAPTER 2. CONVEX GEOMETRYFamili
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88 CHAPTER 2. CONVEX GEOMETRYC 1C 2
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90 CHAPTER 2. CONVEX GEOMETRYA prop
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92 CHAPTER 2. CONVEX GEOMETRY∂K
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94 CHAPTER 2. CONVEX GEOMETRYWhen t
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96 CHAPTER 2. CONVEX GEOMETRYBCADFi
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98 CHAPTER 2. CONVEX GEOMETRYThe po
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104 CHAPTER 2. CONVEX GEOMETRY√2
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106 CHAPTER 2. CONVEX GEOMETRYwhich
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110 CHAPTER 2. CONVEX GEOMETRYA con
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112 CHAPTER 2. CONVEX GEOMETRY0-1-0
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114 CHAPTER 2. CONVEX GEOMETRYposit
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118 CHAPTER 2. CONVEX GEOMETRYThe c
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120 CHAPTER 2. CONVEX GEOMETRYWhen
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122 CHAPTER 2. CONVEX GEOMETRY2.10.
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124 CHAPTER 2. CONVEX GEOMETRY{extr
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126 CHAPTER 2. CONVEX GEOMETRY2.11
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128 CHAPTER 2. CONVEX GEOMETRYFrom
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130 CHAPTER 2. CONVEX GEOMETRYS = {
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132 CHAPTER 2. CONVEX GEOMETRYFigur
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136 CHAPTER 2. CONVEX GEOMETRYK ∗
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138 CHAPTER 2. CONVEX GEOMETRYKK
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140 CHAPTER 2. CONVEX GEOMETRYthe p
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142 CHAPTER 2. CONVEX GEOMETRY(dual
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146 CHAPTER 2. CONVEX GEOMETRYfor w
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148 CHAPTER 2. CONVEX GEOMETRYBy al
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150 CHAPTER 2. CONVEX GEOMETRYb −
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154 CHAPTER 2. CONVEX GEOMETRYDual
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160 CHAPTER 2. CONVEX GEOMETRYΓ 4
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162 CHAPTER 2. CONVEX GEOMETRYEigen
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164 CHAPTER 2. CONVEX GEOMETRYunder
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166 CHAPTER 2. CONVEX GEOMETRYWhen
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168 CHAPTER 2. CONVEX GEOMETRYFor e
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170 CHAPTER 2. CONVEX GEOMETRY10.80
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172 CHAPTER 2. CONVEX GEOMETRYx 210
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174 CHAPTER 2. CONVEX GEOMETRYwhile
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176 CHAPTER 2. CONVEX GEOMETRYαα
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178 CHAPTER 2. CONVEX GEOMETRYFrom
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182 CHAPTER 2. CONVEX GEOMETRYhavin
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184 CHAPTER 3. GEOMETRY OF CONVEX F
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226 CHAPTER 4. SEMIDEFINITE PROGRAM
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292 CHAPTER 5. EUCLIDEAN DISTANCE M
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390 CHAPTER 6. EDM CONEa resemblanc
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392 CHAPTER 6. EDM CONEdvec rel∂E
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394 CHAPTER 6. EDM CONE(b)(c)dvec r
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396 CHAPTER 6. EDM CONE(a)2 nearest
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398 CHAPTER 6. EDM CONEthe graph. T
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400 CHAPTER 6. EDM CONEwhere e i
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402 CHAPTER 6. EDM CONE6.5 EDM defi
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404 CHAPTER 6. EDM CONEN(1 T )δ(V
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406 CHAPTER 6. EDM CONE10(a)-110-1V
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408 CHAPTER 6. EDM CONE6.5.3 Faces
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410 CHAPTER 6. EDM CONE6.5.3.2 Smal
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412 CHAPTER 6. EDM CONE6.6.0.0.1 Pr
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414 CHAPTER 6. EDM CONEdvec rel∂E
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416 CHAPTER 6. EDM CONE6.7 Vectoriz
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418 CHAPTER 6. EDM CONEsvec ∂ S 2
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420 CHAPTER 6. EDM CONEIn fact, the
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422 CHAPTER 6. EDM CONEThe ordinary
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424 CHAPTER 6. EDM CONEEDM 2 = S 2
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426 CHAPTER 6. EDM CONEFrom the res
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428 CHAPTER 6. EDM CONE6.8.1.3 Dual
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430 CHAPTER 6. EDM CONED ◦ = δ(D
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432 CHAPTER 6. EDM CONE6.8.1.6 EDM
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434 CHAPTER 6. EDM CONEBecause 〈
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436 CHAPTER 6. EDM CONE0dvec rel∂
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438 CHAPTER 6. EDM CONE
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440 CHAPTER 7. PROXIMITY PROBLEMS7.
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442 CHAPTER 7. PROXIMITY PROBLEMS..
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444 CHAPTER 7. PROXIMITY PROBLEMSTh
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446 CHAPTER 7. PROXIMITY PROBLEMSwh
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448 CHAPTER 7. PROXIMITY PROBLEMSpo
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452 CHAPTER 7. PROXIMITY PROBLEMSof
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456 CHAPTER 7. PROXIMITY PROBLEMSR
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458 CHAPTER 7. PROXIMITY PROBLEMSwh
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462 CHAPTER 7. PROXIMITY PROBLEMSCo
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466 CHAPTER 7. PROXIMITY PROBLEMSTo
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468 CHAPTER 7. PROXIMITY PROBLEMSth
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470 CHAPTER 7. PROXIMITY PROBLEMSco
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472 CHAPTER 7. PROXIMITY PROBLEMSto
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476 CHAPTER 7. PROXIMITY PROBLEMSdi
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478 CHAPTER 7. PROXIMITY PROBLEMSve
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480 CHAPTER 7. PROXIMITY PROBLEMSth
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482 APPENDIX A. LINEAR ALGEBRAA.1.1
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486 APPENDIX A. LINEAR ALGEBRAonly
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488 APPENDIX A. LINEAR ALGEBRA(AB)
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492 APPENDIX A. LINEAR ALGEBRAFor A
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494 APPENDIX A. LINEAR ALGEBRADiago
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496 APPENDIX A. LINEAR ALGEBRAFor A
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500 APPENDIX A. LINEAR ALGEBRAA.4 S
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504 APPENDIX A. LINEAR ALGEBRAA.5 e
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506 APPENDIX A. LINEAR ALGEBRAs i w
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510 APPENDIX A. LINEAR ALGEBRAΣq 2
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512 APPENDIX A. LINEAR ALGEBRAA.7 Z
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514 APPENDIX A. LINEAR ALGEBRAThere
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518 APPENDIX A. LINEAR ALGEBRA
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520 APPENDIX B. SIMPLE MATRICESB.1
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522 APPENDIX B. SIMPLE MATRICESProo
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524 APPENDIX B. SIMPLE MATRICESB.1.
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526 APPENDIX B. SIMPLE MATRICESN(u
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528 APPENDIX B. SIMPLE MATRICESDue
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532 APPENDIX B. SIMPLE MATRICEShas
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534 APPENDIX B. SIMPLE MATRICESFigu
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538 APPENDIX C. SOME ANALYTICAL OPT
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552 APPENDIX D. MATRIX CALCULUSThe
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554 APPENDIX D. MATRIX CALCULUSGrad
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556 APPENDIX D. MATRIX CALCULUSBeca
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558 APPENDIX D. MATRIX CALCULUSwhic
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560 APPENDIX D. MATRIX CALCULUS⎡
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562 APPENDIX D. MATRIX CALCULUS→Y
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564 APPENDIX D. MATRIX CALCULUSD.1.
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566 APPENDIX D. MATRIX CALCULUSwhic
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568 APPENDIX D. MATRIX CALCULUSIn t
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572 APPENDIX D. MATRIX CALCULUSD.2
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574 APPENDIX D. MATRIX CALCULUSalge
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576 APPENDIX D. MATRIX CALCULUStrac
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580 APPENDIX D. MATRIX CALCULUS
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582 APPENDIX E. PROJECTIONThe follo
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584 APPENDIX E. PROJECTIONFor matri
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586 APPENDIX E. PROJECTION(⇐) To
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588 APPENDIX E. PROJECTIONNonorthog
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590 APPENDIX E. PROJECTIONE.2.0.0.1
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592 APPENDIX E. PROJECTIONE.3.2Orth
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594 APPENDIX E. PROJECTIONE.3.5Unif
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596 APPENDIX E. PROJECTIONE.4 Algeb
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598 APPENDIX E. PROJECTIONa ∗ 2K
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600 APPENDIX E. PROJECTIONwhere Y =
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602 APPENDIX E. PROJECTION(B.4.2).
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604 APPENDIX E. PROJECTIONis a nono
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606 APPENDIX E. PROJECTIONE.6.4.1Or
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608 APPENDIX E. PROJECTIONq i q T i
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610 APPENDIX E. PROJECTIONThe test
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612 APPENDIX E. PROJECTIONPerpendic
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614 APPENDIX E. PROJECTIONE.8 Range
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616 APPENDIX E. PROJECTIONAs for su
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618 APPENDIX E. PROJECTIONWith refe
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620 APPENDIX E. PROJECTIONProjectio
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622 APPENDIX E. PROJECTIONE.9.2.2.2
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624 APPENDIX E. PROJECTIONThe foreg
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626 APPENDIX E. PROJECTION❇❇❇
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628 APPENDIX E. PROJECTIONE.10 Alte
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630 APPENDIX E. PROJECTIONbH 1H 2P
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632 APPENDIX E. PROJECTIONa(a){y |
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634 APPENDIX E. PROJECTION(a feasib
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636 APPENDIX E. PROJECTIONwhile, th
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638 APPENDIX E. PROJECTIONE.10.2.1.
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640 APPENDIX E. PROJECTION10 0dist(
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642 APPENDIX E. PROJECTIONE.10.3.1D
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644 APPENDIX E. PROJECTIONE 3K ⊥
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646 APPENDIX E. PROJECTION
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648 APPENDIX F. MATLAB PROGRAMSif n
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650 APPENDIX F. MATLAB PROGRAMSend%
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652 APPENDIX F. MATLAB PROGRAMSF.1.
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654 APPENDIX F. MATLAB PROGRAMScoun
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656 APPENDIX F. MATLAB PROGRAMSF.3
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660 APPENDIX F. MATLAB PROGRAMS% so
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662 APPENDIX F. MATLAB PROGRAMS% tr
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666 APPENDIX F. MATLAB PROGRAMSbrea
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668 APPENDIX F. MATLAB PROGRAMSwhil
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670 APPENDIX F. MATLAB PROGRAMSF.7
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Page 674 and 675: 674 APPENDIX G. NOTATION AND A FEW
Page 690 and 691: 690 BIBLIOGRAPHY[7] Abdo Y. Alfakih
Page 692 and 693: 692 BIBLIOGRAPHY[27] Aharon Ben-Tal
Page 694 and 695: 694 BIBLIOGRAPHY[48] Lev M. Brègma
Page 696 and 697: 696 BIBLIOGRAPHY[67] Joel Dawson, S
Page 698 and 699: 698 BIBLIOGRAPHY[85] Carl Eckart an
Page 700 and 701: 700 BIBLIOGRAPHY[102] Laurent El Gh
Page 702 and 703: 702 BIBLIOGRAPHY[124] Peter Gritzma
Page 704 and 705: 704 BIBLIOGRAPHY[146] Jean-Baptiste
Page 706 and 707: 706 BIBLIOGRAPHY[168] Jean B. Lasse
Page 708 and 709: 708 BIBLIOGRAPHY[190] Rudolf Mathar
Page 710 and 711: 710 BIBLIOGRAPHY[212] M. L. Overton
Page 712 and 713: 712 BIBLIOGRAPHY[230] R. Tyrrell Ro
Page 714 and 715: 714 BIBLIOGRAPHY[254] Jos F. Sturm
Page 716 and 717: 716 BIBLIOGRAPHY[276] È. B. Vinber
Page 718 and 719: [295] Naoki Yamamoto and Maryam Faz
Page 720 and 721: 720 INDEXobtuse, 62positive semidef
Page 724 and 725: 724 INDEXdiscretization, 152, 185,
Page 726 and 727: 726 INDEXminimization, 206, 611full
Page 728 and 729: 728 INDEXinvariant set, 359inversio
Page 730 and 731: 730 INDEXunitary, 533maximalcomplem
Page 732 and 733: 732 INDEXdifference, 118Farkas’ l
Page 734 and 735: 734 INDEXcommutative, 426, 628direc
Page 736 and 737: 736 INDEXset, 683unique, 42, 185, 1
Page 738: 738 INDEXaffine, 44, 68, 86, 101, 2
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