Attention! Your ePaper is waiting for publication!
By publishing your document, the content will be optimally indexed by Google via AI and sorted into the right category for over 500 million ePaper readers on YUMPU.
This will ensure high visibility and many readers!
Your ePaper is now published and live on YUMPU!
You can find your publication here:
Share your interactive ePaper on all platforms and on your website with our embed function
v2007.09.17 - Convex Optimization
v2007.09.17 - Convex Optimization
v2007.09.17 - Convex Optimization
- No tags were found...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
5.9. BRIDGE: CONVEX POLYHEDRA TO EDMS 351Figure 87: Elliptope E 3 in isometrically isomorphic R 6 (projected on R 3 )is a convex body that appears to possess some kind of symmetry in thisdimension; it resembles a malformed pillow in the shape of a bulgingtetrahedron. Elliptope relative boundary is not smooth and comprises allset members (884) having at least one 0 eigenvalue. [174,2.1] This elliptopehas an infinity of vertices, but there are only four vertices corresponding toa rank-1 matrix. Those yy T , evident in the illustration, have binary vectory ∈ R 3 with entries in {±1}.
350 CHAPTER 5. EUCLIDEAN DISTANCE MATRIX5.9 Bridge: <strong>Convex</strong> polyhedra to EDMsThe criteria for the existence of an EDM include, by definition (709) (774),the properties imposed upon its entries d ij by the Euclidean metric. From5.8.1 and5.8.2, we know there is a relationship of matrix criteria to thoseproperties. Here is a snapshot of what we are sure: for i , j , k ∈{1... N}(confer5.2)√dij ≥ 0, i ≠ j√dij = 0, i = j√dij = √ d ji √dij≤ √ d ik + √ d kj , i≠j ≠k⇐−V T N DV N ≽ 0δ(D) = 0D T = D(882)all implied by D ∈ EDM N . In words, these four Euclidean metric propertiesare necessary conditions for D to be a distance matrix. At the moment,we have no converse. As of concern in5.3, we have yet to establishmetric requirements beyond the four Euclidean metric properties that wouldallow D to be certified an EDM or might facilitate polyhedron or listreconstruction from an incomplete EDM. We deal with this problem in5.14.Our present goal is to establish ab initio the necessary and sufficient matrixcriteria that will subsume all the Euclidean metric properties and any furtherrequirements 5.40 for all N >1 (5.8.3); id est,−V T N DV N ≽ 0D ∈ S N h}⇔ D ∈ EDM N (728)or for EDM definition (783),}Ω ≽ 0√δ(d) ≽ 0⇔ D = D(Ω,d) ∈ EDM N (883)5.40 In 1935, Schoenberg [234, (1)] first extolled matrix product −VN TDV N (862)(predicated on symmetry and self-distance) specifically incorporating V N , albeitalgebraically. He showed: nonnegativity −y T VN TDV N y ≥ 0, for all y ∈ R N−1 , is necessaryand sufficient for D to be an EDM. Gower [112,3] remarks how surprising it is that sucha fundamental property of Euclidean geometry was obtained so late.
5.9. BRIDGE: CONVEX POLYHEDRA TO EDMS 351Figure 87: Elliptope E 3 in isometrically isomorphic R 6 (projected on R 3 )is a convex body that appears to possess some kind of symmetry in thisdimension; it resembles a malformed pillow in the shape of a bulgingtetrahedron. Elliptope relative boundary is not smooth and comprises allset members (884) having at least one 0 eigenvalue. [174,2.1] This elliptopehas an infinity of vertices, but there are only four vertices corresponding toa rank-1 matrix. Those yy T , evident in the illustration, have binary vectory ∈ R 3 with entries in {±1}.
- Page 2 and 3:
DattorroCONVEXOPTIMIZATION&EUCLIDEA
- Page 4 and 5:
Meboo Publishing USA345 Stanford Sh
- Page 6 and 7:
EDM = S h ∩ ( S ⊥ c − S +)
- Page 8 and 9:
There is a great race under way to
- Page 10 and 11:
10 CONVEX OPTIMIZATION & EUCLIDEAN
- Page 12 and 13:
12 CONVEX OPTIMIZATION & EUCLIDEAN
- Page 14 and 15:
14 LIST OF FIGURES24 Nonconvex cone
- Page 16 and 17:
16 LIST OF FIGURES92 Largest ten ei
- Page 18 and 19:
List of Tables2 Convex geometryTabl
- Page 20 and 21:
20 CHAPTER 1. OVERVIEWFigure 1: Ori
- Page 22 and 23:
22 CHAPTER 1. OVERVIEWFigure 3: [13
- Page 24 and 25:
24 CHAPTER 1. OVERVIEWFigure 5: Swi
- Page 26 and 27:
26 CHAPTER 1. OVERVIEWoriginalrecon
- Page 28 and 29:
28 CHAPTER 1. OVERVIEWFigure 8: Rob
- Page 30 and 31:
30 CHAPTER 1. OVERVIEWnoveltyp.120
- Page 32 and 33:
32 CHAPTER 1. OVERVIEW
- Page 34 and 35:
34 CHAPTER 2. CONVEX GEOMETRY2.1 Co
- Page 36 and 37:
36 CHAPTER 2. CONVEX GEOMETRY2.1.3
- Page 38 and 39:
38 CHAPTER 2. CONVEX GEOMETRY(a)R(b
- Page 40 and 41:
40 CHAPTER 2. CONVEX GEOMETRYwhere
- Page 42 and 43:
42 CHAPTER 2. CONVEX GEOMETRYNow le
- Page 44 and 45:
44 CHAPTER 2. CONVEX GEOMETRY2.1.9
- Page 46 and 47:
46 CHAPTER 2. CONVEX GEOMETRYand wh
- Page 48 and 49:
48 CHAPTER 2. CONVEX GEOMETRY2.2.1.
- Page 50 and 51:
50 CHAPTER 2. CONVEX GEOMETRYwhere
- Page 52 and 53:
52 CHAPTER 2. CONVEX GEOMETRYAny ma
- Page 54 and 55:
54 CHAPTER 2. CONVEX GEOMETRYIn par
- Page 56 and 57:
56 CHAPTER 2. CONVEX GEOMETRY2.3.1.
- Page 58 and 59:
58 CHAPTER 2. CONVEX GEOMETRYsvec
- Page 60 and 61:
60 CHAPTER 2. CONVEX GEOMETRYFigure
- Page 62 and 63:
62 CHAPTER 2. CONVEX GEOMETRY2.4.1
- Page 64 and 65:
64 CHAPTER 2. CONVEX GEOMETRY11−1
- Page 66 and 67:
66 CHAPTER 2. CONVEX GEOMETRYHyperp
- Page 68 and 69:
68 CHAPTER 2. CONVEX GEOMETRYCH −
- Page 70 and 71:
70 CHAPTER 2. CONVEX GEOMETRYnonemp
- Page 72 and 73:
72 CHAPTER 2. CONVEX GEOMETRYto vec
- Page 74 and 75:
74 CHAPTER 2. CONVEX GEOMETRY2.5.1
- Page 76 and 77:
76 CHAPTER 2. CONVEX GEOMETRY2.5.2
- Page 78 and 79:
78 CHAPTER 2. CONVEX GEOMETRYABCDFi
- Page 80 and 81:
80 CHAPTER 2. CONVEX GEOMETRY2.6.1.
- Page 82 and 83:
82 CHAPTER 2. CONVEX GEOMETRYX(a)00
- Page 84 and 85:
84 CHAPTER 2. CONVEX GEOMETRYXXFigu
- Page 86 and 87:
86 CHAPTER 2. CONVEX GEOMETRYFamili
- Page 88 and 89:
88 CHAPTER 2. CONVEX GEOMETRYC 1C 2
- Page 90 and 91:
90 CHAPTER 2. CONVEX GEOMETRYA prop
- Page 92 and 93:
92 CHAPTER 2. CONVEX GEOMETRY∂K
- Page 94 and 95:
94 CHAPTER 2. CONVEX GEOMETRYWhen t
- Page 96 and 97:
96 CHAPTER 2. CONVEX GEOMETRYBCADFi
- Page 98 and 99:
98 CHAPTER 2. CONVEX GEOMETRYThe po
- Page 100 and 101:
100 CHAPTER 2. CONVEX GEOMETRY2.9.0
- Page 102 and 103:
102 CHAPTER 2. CONVEX GEOMETRYwhere
- Page 104 and 105:
104 CHAPTER 2. CONVEX GEOMETRY√2
- Page 106 and 107:
106 CHAPTER 2. CONVEX GEOMETRYwhich
- Page 108 and 109:
108 CHAPTER 2. CONVEX GEOMETRY2.9.2
- Page 110 and 111:
110 CHAPTER 2. CONVEX GEOMETRYA con
- Page 112 and 113:
112 CHAPTER 2. CONVEX GEOMETRY0-1-0
- Page 114 and 115:
114 CHAPTER 2. CONVEX GEOMETRYposit
- Page 116 and 117:
116 CHAPTER 2. CONVEX GEOMETRY2.9.2
- Page 118 and 119:
118 CHAPTER 2. CONVEX GEOMETRYThe c
- Page 120 and 121:
120 CHAPTER 2. CONVEX GEOMETRYWhen
- Page 122 and 123:
122 CHAPTER 2. CONVEX GEOMETRY2.10.
- Page 124 and 125:
124 CHAPTER 2. CONVEX GEOMETRY{extr
- Page 126 and 127:
126 CHAPTER 2. CONVEX GEOMETRY2.11
- Page 128 and 129:
128 CHAPTER 2. CONVEX GEOMETRYFrom
- Page 130 and 131:
130 CHAPTER 2. CONVEX GEOMETRYS = {
- Page 132 and 133:
132 CHAPTER 2. CONVEX GEOMETRYFigur
- Page 134 and 135:
134 CHAPTER 2. CONVEX GEOMETRY2.12.
- Page 136 and 137:
136 CHAPTER 2. CONVEX GEOMETRYK ∗
- Page 138 and 139:
138 CHAPTER 2. CONVEX GEOMETRYKK
- Page 140 and 141:
140 CHAPTER 2. CONVEX GEOMETRYthe p
- Page 142 and 143:
142 CHAPTER 2. CONVEX GEOMETRY(dual
- Page 144 and 145:
144 CHAPTER 2. CONVEX GEOMETRY2.13.
- Page 146 and 147:
146 CHAPTER 2. CONVEX GEOMETRYfor w
- Page 148 and 149:
148 CHAPTER 2. CONVEX GEOMETRYBy al
- Page 150 and 151:
150 CHAPTER 2. CONVEX GEOMETRYb −
- Page 152 and 153:
152 CHAPTER 2. CONVEX GEOMETRY2.13.
- Page 154 and 155:
154 CHAPTER 2. CONVEX GEOMETRYDual
- Page 156 and 157:
156 CHAPTER 2. CONVEX GEOMETRY2.13.
- Page 158 and 159:
158 CHAPTER 2. CONVEX GEOMETRY2.13.
- Page 160 and 161:
160 CHAPTER 2. CONVEX GEOMETRYΓ 4
- Page 162 and 163:
162 CHAPTER 2. CONVEX GEOMETRYEigen
- Page 164 and 165:
164 CHAPTER 2. CONVEX GEOMETRYunder
- Page 166 and 167:
166 CHAPTER 2. CONVEX GEOMETRYWhen
- Page 168 and 169:
168 CHAPTER 2. CONVEX GEOMETRYFor e
- Page 170 and 171:
170 CHAPTER 2. CONVEX GEOMETRY10.80
- Page 172 and 173:
172 CHAPTER 2. CONVEX GEOMETRYx 210
- Page 174 and 175:
174 CHAPTER 2. CONVEX GEOMETRYwhile
- Page 176 and 177:
176 CHAPTER 2. CONVEX GEOMETRYαα
- Page 178 and 179:
178 CHAPTER 2. CONVEX GEOMETRYFrom
- Page 180 and 181:
180 CHAPTER 2. CONVEX GEOMETRY2.13.
- Page 182 and 183:
182 CHAPTER 2. CONVEX GEOMETRYhavin
- Page 184 and 185:
184 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 186 and 187:
186 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 188 and 189:
188 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 190 and 191:
190 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 192 and 193:
192 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 194 and 195:
194 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 196 and 197:
196 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 198 and 199:
198 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 200 and 201:
200 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 202 and 203:
202 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 204 and 205:
204 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 206 and 207:
206 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 208 and 209:
208 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 210 and 211:
210 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 212 and 213:
212 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 214 and 215:
214 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 216 and 217:
216 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 218 and 219:
218 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 220 and 221:
220 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 222 and 223:
222 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 224 and 225:
224 CHAPTER 3. GEOMETRY OF CONVEX F
- Page 226 and 227:
226 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 228 and 229:
228 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 230 and 231:
230 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 232 and 233:
232 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 234 and 235:
234 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 236 and 237:
236 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 238 and 239:
238 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 240 and 241:
240 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 242 and 243:
242 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 244 and 245:
244 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 246 and 247:
246 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 248 and 249:
248 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 250 and 251:
250 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 252 and 253:
252 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 254 and 255:
254 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 256 and 257:
256 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 258 and 259:
258 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 260 and 261:
260 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 262 and 263:
262 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 264 and 265:
264 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 266 and 267:
266 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 268 and 269:
268 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 270 and 271:
270 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 272 and 273:
272 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 274 and 275:
274 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 276 and 277:
276 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 278 and 279:
278 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 280 and 281:
280 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 282 and 283:
282 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 284 and 285:
284 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 286 and 287:
286 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 288 and 289:
288 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 290 and 291:
290 CHAPTER 4. SEMIDEFINITE PROGRAM
- Page 292 and 293:
292 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 294 and 295:
294 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 296 and 297:
296 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 298 and 299:
298 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 300 and 301: 300 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 302 and 303: 302 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 304 and 305: 304 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 306 and 307: 306 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 308 and 309: 308 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 310 and 311: 310 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 312 and 313: 312 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 314 and 315: 314 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 316 and 317: 316 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 318 and 319: 318 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 320 and 321: 320 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 322 and 323: 322 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 324 and 325: 324 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 326 and 327: 326 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 328 and 329: 328 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 330 and 331: 330 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 332 and 333: 332 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 334 and 335: 334 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 336 and 337: 336 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 338 and 339: 338 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 340 and 341: 340 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 342 and 343: 342 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 344 and 345: 344 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 346 and 347: 346 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 348 and 349: 348 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 352 and 353: 352 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 354 and 355: 354 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 356 and 357: 356 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 358 and 359: 358 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 360 and 361: 360 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 362 and 363: 362 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 364 and 365: 364 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 366 and 367: 366 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 368 and 369: 368 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 370 and 371: 370 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 372 and 373: 372 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 374 and 375: 374 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 376 and 377: 376 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 378 and 379: 378 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 380 and 381: 380 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 382 and 383: 382 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 384 and 385: 384 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 386 and 387: 386 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 388 and 389: 388 CHAPTER 5. EUCLIDEAN DISTANCE M
- Page 390 and 391: 390 CHAPTER 6. EDM CONEa resemblanc
- Page 392 and 393: 392 CHAPTER 6. EDM CONEdvec rel∂E
- Page 394 and 395: 394 CHAPTER 6. EDM CONE(b)(c)dvec r
- Page 396 and 397: 396 CHAPTER 6. EDM CONE(a)2 nearest
- Page 398 and 399: 398 CHAPTER 6. EDM CONEthe graph. T
- Page 400 and 401:
400 CHAPTER 6. EDM CONEwhere e i
- Page 402 and 403:
402 CHAPTER 6. EDM CONE6.5 EDM defi
- Page 404 and 405:
404 CHAPTER 6. EDM CONEN(1 T )δ(V
- Page 406 and 407:
406 CHAPTER 6. EDM CONE10(a)-110-1V
- Page 408 and 409:
408 CHAPTER 6. EDM CONE6.5.3 Faces
- Page 410 and 411:
410 CHAPTER 6. EDM CONE6.5.3.2 Smal
- Page 412 and 413:
412 CHAPTER 6. EDM CONE6.6.0.0.1 Pr
- Page 414 and 415:
414 CHAPTER 6. EDM CONEdvec rel∂E
- Page 416 and 417:
416 CHAPTER 6. EDM CONE6.7 Vectoriz
- Page 418 and 419:
418 CHAPTER 6. EDM CONEsvec ∂ S 2
- Page 420 and 421:
420 CHAPTER 6. EDM CONEIn fact, the
- Page 422 and 423:
422 CHAPTER 6. EDM CONEThe ordinary
- Page 424 and 425:
424 CHAPTER 6. EDM CONEEDM 2 = S 2
- Page 426 and 427:
426 CHAPTER 6. EDM CONEFrom the res
- Page 428 and 429:
428 CHAPTER 6. EDM CONE6.8.1.3 Dual
- Page 430 and 431:
430 CHAPTER 6. EDM CONED ◦ = δ(D
- Page 432 and 433:
432 CHAPTER 6. EDM CONE6.8.1.6 EDM
- Page 434 and 435:
434 CHAPTER 6. EDM CONEBecause 〈
- Page 436 and 437:
436 CHAPTER 6. EDM CONE0dvec rel∂
- Page 438 and 439:
438 CHAPTER 6. EDM CONE
- Page 440 and 441:
440 CHAPTER 7. PROXIMITY PROBLEMS7.
- Page 442 and 443:
442 CHAPTER 7. PROXIMITY PROBLEMS..
- Page 444 and 445:
444 CHAPTER 7. PROXIMITY PROBLEMSTh
- Page 446 and 447:
446 CHAPTER 7. PROXIMITY PROBLEMSwh
- Page 448 and 449:
448 CHAPTER 7. PROXIMITY PROBLEMSpo
- Page 450 and 451:
450 CHAPTER 7. PROXIMITY PROBLEMS7.
- Page 452 and 453:
452 CHAPTER 7. PROXIMITY PROBLEMSof
- Page 454 and 455:
454 CHAPTER 7. PROXIMITY PROBLEMS7.
- Page 456 and 457:
456 CHAPTER 7. PROXIMITY PROBLEMSR
- Page 458 and 459:
458 CHAPTER 7. PROXIMITY PROBLEMSwh
- Page 460 and 461:
460 CHAPTER 7. PROXIMITY PROBLEMS7.
- Page 462 and 463:
462 CHAPTER 7. PROXIMITY PROBLEMSCo
- Page 464 and 465:
464 CHAPTER 7. PROXIMITY PROBLEMS7.
- Page 466 and 467:
466 CHAPTER 7. PROXIMITY PROBLEMSTo
- Page 468 and 469:
468 CHAPTER 7. PROXIMITY PROBLEMSth
- Page 470 and 471:
470 CHAPTER 7. PROXIMITY PROBLEMSco
- Page 472 and 473:
472 CHAPTER 7. PROXIMITY PROBLEMSto
- Page 474 and 475:
474 CHAPTER 7. PROXIMITY PROBLEMS7.
- Page 476 and 477:
476 CHAPTER 7. PROXIMITY PROBLEMSdi
- Page 478 and 479:
478 CHAPTER 7. PROXIMITY PROBLEMSve
- Page 480 and 481:
480 CHAPTER 7. PROXIMITY PROBLEMSth
- Page 482 and 483:
482 APPENDIX A. LINEAR ALGEBRAA.1.1
- Page 484 and 485:
484 APPENDIX A. LINEAR ALGEBRAA.1.2
- Page 486 and 487:
486 APPENDIX A. LINEAR ALGEBRAonly
- Page 488 and 489:
488 APPENDIX A. LINEAR ALGEBRA(AB)
- Page 490 and 491:
490 APPENDIX A. LINEAR ALGEBRAA.3.1
- Page 492 and 493:
492 APPENDIX A. LINEAR ALGEBRAFor A
- Page 494 and 495:
494 APPENDIX A. LINEAR ALGEBRADiago
- Page 496 and 497:
496 APPENDIX A. LINEAR ALGEBRAFor A
- Page 498 and 499:
498 APPENDIX A. LINEAR ALGEBRAA.3.1
- Page 500 and 501:
500 APPENDIX A. LINEAR ALGEBRAA.4 S
- Page 502 and 503:
502 APPENDIX A. LINEAR ALGEBRAA.4.0
- Page 504 and 505:
504 APPENDIX A. LINEAR ALGEBRAA.5 e
- Page 506 and 507:
506 APPENDIX A. LINEAR ALGEBRAs i w
- Page 508 and 509:
508 APPENDIX A. LINEAR ALGEBRAA.6.2
- Page 510 and 511:
510 APPENDIX A. LINEAR ALGEBRAΣq 2
- Page 512 and 513:
512 APPENDIX A. LINEAR ALGEBRAA.7 Z
- Page 514 and 515:
514 APPENDIX A. LINEAR ALGEBRAThere
- Page 516 and 517:
516 APPENDIX A. LINEAR ALGEBRAA.7.5
- Page 518 and 519:
518 APPENDIX A. LINEAR ALGEBRA
- Page 520 and 521:
520 APPENDIX B. SIMPLE MATRICESB.1
- Page 522 and 523:
522 APPENDIX B. SIMPLE MATRICESProo
- Page 524 and 525:
524 APPENDIX B. SIMPLE MATRICESB.1.
- Page 526 and 527:
526 APPENDIX B. SIMPLE MATRICESN(u
- Page 528 and 529:
528 APPENDIX B. SIMPLE MATRICESDue
- Page 530 and 531:
530 APPENDIX B. SIMPLE MATRICESB.4.
- Page 532 and 533:
532 APPENDIX B. SIMPLE MATRICEShas
- Page 534 and 535:
534 APPENDIX B. SIMPLE MATRICESFigu
- Page 536 and 537:
536 APPENDIX B. SIMPLE MATRICESB.5.
- Page 538 and 539:
538 APPENDIX C. SOME ANALYTICAL OPT
- Page 540 and 541:
540 APPENDIX C. SOME ANALYTICAL OPT
- Page 542 and 543:
542 APPENDIX C. SOME ANALYTICAL OPT
- Page 544 and 545:
544 APPENDIX C. SOME ANALYTICAL OPT
- Page 546 and 547:
546 APPENDIX C. SOME ANALYTICAL OPT
- Page 548 and 549:
548 APPENDIX C. SOME ANALYTICAL OPT
- Page 550 and 551:
550 APPENDIX C. SOME ANALYTICAL OPT
- Page 552 and 553:
552 APPENDIX D. MATRIX CALCULUSThe
- Page 554 and 555:
554 APPENDIX D. MATRIX CALCULUSGrad
- Page 556 and 557:
556 APPENDIX D. MATRIX CALCULUSBeca
- Page 558 and 559:
558 APPENDIX D. MATRIX CALCULUSwhic
- Page 560 and 561:
560 APPENDIX D. MATRIX CALCULUS⎡
- Page 562 and 563:
562 APPENDIX D. MATRIX CALCULUS→Y
- Page 564 and 565:
564 APPENDIX D. MATRIX CALCULUSD.1.
- Page 566 and 567:
566 APPENDIX D. MATRIX CALCULUSwhic
- Page 568 and 569:
568 APPENDIX D. MATRIX CALCULUSIn t
- Page 570 and 571:
570 APPENDIX D. MATRIX CALCULUSD.1.
- Page 572 and 573:
572 APPENDIX D. MATRIX CALCULUSD.2
- Page 574 and 575:
574 APPENDIX D. MATRIX CALCULUSalge
- Page 576 and 577:
576 APPENDIX D. MATRIX CALCULUStrac
- Page 578 and 579:
578 APPENDIX D. MATRIX CALCULUSD.2.
- Page 580 and 581:
580 APPENDIX D. MATRIX CALCULUS
- Page 582 and 583:
582 APPENDIX E. PROJECTIONThe follo
- Page 584 and 585:
584 APPENDIX E. PROJECTIONFor matri
- Page 586 and 587:
586 APPENDIX E. PROJECTION(⇐) To
- Page 588 and 589:
588 APPENDIX E. PROJECTIONNonorthog
- Page 590 and 591:
590 APPENDIX E. PROJECTIONE.2.0.0.1
- Page 592 and 593:
592 APPENDIX E. PROJECTIONE.3.2Orth
- Page 594 and 595:
594 APPENDIX E. PROJECTIONE.3.5Unif
- Page 596 and 597:
596 APPENDIX E. PROJECTIONE.4 Algeb
- Page 598 and 599:
598 APPENDIX E. PROJECTIONa ∗ 2K
- Page 600 and 601:
600 APPENDIX E. PROJECTIONwhere Y =
- Page 602 and 603:
602 APPENDIX E. PROJECTION(B.4.2).
- Page 604 and 605:
604 APPENDIX E. PROJECTIONis a nono
- Page 606 and 607:
606 APPENDIX E. PROJECTIONE.6.4.1Or
- Page 608 and 609:
608 APPENDIX E. PROJECTIONq i q T i
- Page 610 and 611:
610 APPENDIX E. PROJECTIONThe test
- Page 612 and 613:
612 APPENDIX E. PROJECTIONPerpendic
- Page 614 and 615:
614 APPENDIX E. PROJECTIONE.8 Range
- Page 616 and 617:
616 APPENDIX E. PROJECTIONAs for su
- Page 618 and 619:
618 APPENDIX E. PROJECTIONWith refe
- Page 620 and 621:
620 APPENDIX E. PROJECTIONProjectio
- Page 622 and 623:
622 APPENDIX E. PROJECTIONE.9.2.2.2
- Page 624 and 625:
624 APPENDIX E. PROJECTIONThe foreg
- Page 626 and 627:
626 APPENDIX E. PROJECTION❇❇❇
- Page 628 and 629:
628 APPENDIX E. PROJECTIONE.10 Alte
- Page 630 and 631:
630 APPENDIX E. PROJECTIONbH 1H 2P
- Page 632 and 633:
632 APPENDIX E. PROJECTIONa(a){y |
- Page 634 and 635:
634 APPENDIX E. PROJECTION(a feasib
- Page 636 and 637:
636 APPENDIX E. PROJECTIONwhile, th
- Page 638 and 639:
638 APPENDIX E. PROJECTIONE.10.2.1.
- Page 640 and 641:
640 APPENDIX E. PROJECTION10 0dist(
- Page 642 and 643:
642 APPENDIX E. PROJECTIONE.10.3.1D
- Page 644 and 645:
644 APPENDIX E. PROJECTIONE 3K ⊥
- Page 646 and 647:
646 APPENDIX E. PROJECTION
- Page 648 and 649:
648 APPENDIX F. MATLAB PROGRAMSif n
- Page 650 and 651:
650 APPENDIX F. MATLAB PROGRAMSend%
- Page 652 and 653:
652 APPENDIX F. MATLAB PROGRAMSF.1.
- Page 654 and 655:
654 APPENDIX F. MATLAB PROGRAMScoun
- Page 656 and 657:
656 APPENDIX F. MATLAB PROGRAMSF.3
- Page 658 and 659:
658 APPENDIX F. MATLAB PROGRAMSF.3.
- Page 660 and 661:
660 APPENDIX F. MATLAB PROGRAMS% so
- Page 662 and 663:
662 APPENDIX F. MATLAB PROGRAMS% tr
- Page 664 and 665:
664 APPENDIX F. MATLAB PROGRAMSF.4.
- Page 666 and 667:
666 APPENDIX F. MATLAB PROGRAMSbrea
- Page 668 and 669:
668 APPENDIX F. MATLAB PROGRAMSwhil
- Page 670 and 671:
670 APPENDIX F. MATLAB PROGRAMSF.7
- Page 672 and 673:
672 APPENDIX F. MATLAB PROGRAMS
- Page 674 and 675:
674 APPENDIX G. NOTATION AND A FEW
- Page 676 and 677:
676 APPENDIX G. NOTATION AND A FEW
- Page 678 and 679:
678 APPENDIX G. NOTATION AND A FEW
- Page 680 and 681:
680 APPENDIX G. NOTATION AND A FEW
- Page 682 and 683:
682 APPENDIX G. NOTATION AND A FEW
- Page 684 and 685:
684 APPENDIX G. NOTATION AND A FEW
- Page 686 and 687:
686 APPENDIX G. NOTATION AND A FEW
- Page 688 and 689:
688 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 722 and 723:
722 INDEXnormal, 175, 415, 622, 642
- 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
Inappropriate
Loading...
Inappropriate
You have already flagged this document.
Thank you, for helping us keep this platform clean.
The editors will have a look at it as soon as possible.
Mail this publication
Loading...
Embed
Loading...
Delete template?
Are you sure you want to delete your template?
DOWNLOAD ePAPER
This ePaper is currently not available for download.
You can find similar magazines on this topic below under ‘Recommendations’.