v2004.06.19 - Convex Optimization

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272 CHAPTER 7. EDM PROXIMITY
Chapter 8EDM completionIt is not known how to proceed if one wishes to restrict the dimensionof the Euclidean space in which the configuration of pointsmay be constructed.−Michael W. Trosset, 2000 [47]Intriguing is the question of whether the list in X ∈ R n×N (54) may bereconstructed given an incomplete EDM, and under what circumstances thereconstruction is unique. In this chapter we assume an EDM is only partiallyknown, and the known entries are noiseless. 8.1 Due to translation invarianceof an EDM (§4.5), we need only consider reconstruction in subspace R r wherer is affine dimension.We examined this completion problem for small Example 4.3.0.0.2(p.132); revisited in §4.9.3 and §4.12.4.1. When the cardinality N exceeds 4,it is no longer sufficient or convenient to use the fifth Euclidean axiom as wedid in §4.12.4.1; we need a universal theory.8.0 c○ 2001 Jon Dattorro, all rights reserved.8.1 Unknown entries may, for example, be constrained by upper and lower bounds; indeed,all the entries might be unknown having bound constraints.273
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Euclidean Distance GeometryviaConve
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for Jennie Columba♦♦Antonio♦a
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illustrations: Mayura Drawtypesetti
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8 CONTENTS2.7 Convex polyhedra . .
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10 CONTENTS5.3 EDM cone by inverse
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12 CONTENTSB.2 Doublet . . . . . .
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14 CONTENTSG Notation and some defi
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16 CHAPTER 1. PRELUDEThese pages co
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18 CHAPTER 1. PRELUDEChapter 8 inve
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20 CHAPTER 2. CONVEX GEOMETRY2.1 Co
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22 CHAPTER 2. CONVEX GEOMETRY(a)R(b
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24 CHAPTER 2. CONVEX GEOMETRYTogeth
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26 CHAPTER 2. CONVEX GEOMETRYand wh
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28 CHAPTER 2. CONVEX GEOMETRY2.1.2
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30 CHAPTER 2. CONVEX GEOMETRYwhere
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32 CHAPTER 2. CONVEX GEOMETRYLike b
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34 CHAPTER 2. CONVEX GEOMETRYGiven
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36 CHAPTER 2. CONVEX GEOMETRYGiven
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38 CHAPTER 2. CONVEX GEOMETRYThis r
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42 CHAPTER 2. CONVEX GEOMETRY(a)Yy
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44 CHAPTER 2. CONVEX GEOMETRY1) If
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46 CHAPTER 2. CONVEX GEOMETRY2.4.1.
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48 CHAPTER 2. CONVEX GEOMETRYABCDFi
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50 CHAPTER 2. CONVEX GEOMETRYAn aff
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52 CHAPTER 2. CONVEX GEOMETRYXXFigu
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54 CHAPTER 2. CONVEX GEOMETRYcone S
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58 CHAPTER 2. CONVEX GEOMETRYBCADFi
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64 CHAPTER 2. CONVEX GEOMETRY√2β
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66 CHAPTER 2. CONVEX GEOMETRYwhich
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68 CHAPTER 2. CONVEX GEOMETRYequals
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70 CHAPTER 2. CONVEX GEOMETRYAssumi
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74 CHAPTER 2. CONVEX GEOMETRYFrom t
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76 CHAPTER 2. CONVEX GEOMETRYFor an
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80 CHAPTER 2. CONVEX GEOMETRY• (S
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82 CHAPTER 2. CONVEX GEOMETRYmerely
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84 CHAPTER 2. CONVEX GEOMETRYy ∈
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88 CHAPTER 2. CONVEX GEOMETRYthat f
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90 CHAPTER 2. CONVEX GEOMETRYWhen X
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92 CHAPTER 2. CONVEX GEOMETRY2.9 Fo
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94 CHAPTER 2. CONVEX GEOMETRYFor γ
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96 CHAPTER 2. CONVEX GEOMETRYConver
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98 CHAPTER 2. CONVEX GEOMETRYAssume
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100 CHAPTER 2. CONVEX GEOMETRYwhere
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102 CHAPTER 2. CONVEX GEOMETRYbiort
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X 1 =4X †T1 =⎡⎢⎣⎡⎢⎣10
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106 CHAPTER 2. CONVEX GEOMETRYFigur
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108 CHAPTER 2. CONVEX GEOMETRY∂K
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110 CHAPTER 2. CONVEX GEOMETRYΓ 4
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112 CHAPTER 2. CONVEX GEOMETRY∂K
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114 CHAPTER 3. GEOMETRY OF CONVEX F
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130 CHAPTER 4. EUCLIDEAN DISTANCE M
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204 CHAPTER 5. EDM CONEFor now we i
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206 CHAPTER 5. EDM CONE5.1 Polyhedr
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208 CHAPTER 5. EDM CONE5.2.1 Range
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210 CHAPTER 5. EDM CONEA statement
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212 CHAPTER 5. EDM CONEIn particula
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214 CHAPTER 5. EDM CONE5.4 Correspo
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216 CHAPTER 5. EDM CONE5.4.2 Monoto
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218 CHAPTER 5. EDM CONEsvec ∂ S 2
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220 CHAPTER 5. EDM CONE5.6 Dual EDM
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Page 244 and 245: 244 CHAPTER 7. EDM PROXIMITY7.0.1 L
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Page 292 and 293: 292 APPENDIX A. LINEAR ALGEBRAmatri
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322 APPENDIX A. LINEAR ALGEBRAwhich
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324 APPENDIX A. LINEAR ALGEBRA
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326 APPENDIX B. SIMPLE MATRICESB.1
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328 APPENDIX B. SIMPLE MATRICESB.1.
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330 APPENDIX B. SIMPLE MATRICESby t
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332 APPENDIX B. SIMPLE MATRICESN(u
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334 APPENDIX B. SIMPLE MATRICESthe
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340 APPENDIX B. SIMPLE MATRICESThis
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342 APPENDIX B. SIMPLE MATRICES
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344 APPENDIX C. SOME OPTIMAL ANALYT
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352 APPENDIX D. MATRIX CALCULUSwhil
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354 APPENDIX D. MATRIX CALCULUSa cu
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356 APPENDIX D. MATRIX CALCULUSprod
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358 APPENDIX D. MATRIX CALCULUS∇
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360 APPENDIX D. MATRIX CALCULUSin m
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362 APPENDIX D. MATRIX CALCULUSNoti
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364 APPENDIX D. MATRIX CALCULUS⎡
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366 APPENDIX D. MATRIX CALCULUSD.1.
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368 APPENDIX D. MATRIX CALCULUSExam
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370 APPENDIX D. MATRIX CALCULUSD.2
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372 APPENDIX D. MATRIX CALCULUS
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382 APPENDIX D. MATRIX CALCULUS
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384 APPENDIX E. PSEUDOINVERSE, PROJ
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436 APPENDIX F. MATLAB PROGRAMS...F
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438 APPENDIX F. MATLAB PROGRAMS...F
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440 APPENDIX F. MATLAB PROGRAMS...l
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442 APPENDIX F. MATLAB PROGRAMS...s
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444 APPENDIX F. MATLAB PROGRAMS...
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446 APPENDIX G. NOTATION AND SOME D
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456 BIBLIOGRAPHY[9] Günter M. Zieg
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458 BIBLIOGRAPHY[28] Roger A. Horn
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460 BIBLIOGRAPHY[54] Hong-Xuan Huan
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462 BIBLIOGRAPHY[76] Peter Gritzman
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464 BIBLIOGRAPHYtors, Handbook of S
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466 BIBLIOGRAPHY[117] Shao-Po Wu an
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468 BIBLIOGRAPHY[134] Maryam Fazel,
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470 BIBLIOGRAPHY[154] George P. H.
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472 BIBLIOGRAPHY[178] Jean-Baptiste
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474 BIBLIOGRAPHY
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