v2010.10.26 - Convex Optimization
v2010.10.26 - Convex Optimization v2010.10.26 - Convex Optimization
320 CHAPTER 4. SEMIDEFINITE PROGRAMMING5 763 841 92Figure 87: 3-lattice in R 2 , hand-drawn. Nodes 7, 8, and 9 are anchors;remaining nodes are sensors. Radio range of sensor 1 indicated by arc.range of possible distance for each measurable distance; equality constraintsexist only for anchors.Anchors are chosen so as to increase difficulty for algorithms dependenton existence of sensors in their convex hull. The challenge is to find a solutionin two dimensions close to the true sensor positions given incomplete noisyintersensor distance information.0 • • ? • ? ? • •• 0 • • ? • ? • •• • 0 • • • • • •? • • 0 ? • • • •• ? • ? 0 • • • •? • • • • 0 • • •? ? • • • • 0 ◦ ◦• • • • • • ◦ 0 ◦• • • • • • ◦ ◦ 0(747)
4.4. RANK-CONSTRAINED SEMIDEFINITE PROGRAM 3211013 11 1271489415 5 611623Figure 88: 4-lattice in R 2 , hand-drawn. Nodes 13, 14, 15, and 16 are anchors;remaining nodes are sensors. Radio range of sensor 1 indicated by arc.0 ? ? • ? ? • ? ? ? ? ? ? ? • •? 0 • • • • ? • ? ? ? ? ? • • •? • 0 ? • • ? ? • ? ? ? ? ? • •• • ? 0 • ? • • ? • ? ? • • • •? • • • 0 • ? • • ? • • • • • •? • • ? • 0 ? • • ? • • ? ? ? ?• ? ? • ? ? 0 ? ? • ? ? • • • •? • ? • • • ? 0 • • • • • • • •? ? • ? • • ? • 0 ? • • • ? • ?? ? ? • ? ? • • ? 0 • ? • • • ?? ? ? ? • • ? • • • 0 • • • • ?? ? ? ? • • ? • • ? • 0 ? ? ? ?? ? ? • • ? • • • • • ? 0 ◦ ◦ ◦? • ? • • ? • • ? • • ? ◦ 0 ◦ ◦• • • • • ? • • • • • ? ◦ ◦ 0 ◦• • • • • ? • • ? ? ? ? ◦ ◦ ◦ 0(748)
- Page 269 and 270: 3.8. QUASICONVEX 269exponential alw
- Page 271 and 272: 3.9. SALIENT PROPERTIES 2713.8.0.0.
- Page 273 and 274: Chapter 4Semidefinite programmingPr
- Page 275 and 276: 4.1. CONIC PROBLEM 275(confer p.162
- Page 277 and 278: 4.1. CONIC PROBLEM 277PCsemidefinit
- Page 279 and 280: 4.1. CONIC PROBLEM 279is the affine
- Page 281 and 282: 4.1. CONIC PROBLEM 281faces of S 3
- Page 283 and 284: 4.1. CONIC PROBLEM 2834.1.2.3 Previ
- Page 285 and 286: 4.2. FRAMEWORK 285Semidefinite Fark
- Page 287 and 288: 4.2. FRAMEWORK 287On the other hand
- Page 289 and 290: 4.2. FRAMEWORK 2894.2.2.1 Dual prob
- Page 291 and 292: 4.2. FRAMEWORK 291For symmetric pos
- Page 293 and 294: 4.2. FRAMEWORK 293has norm ‖x ⋆
- Page 295 and 296: 4.2. FRAMEWORK 295minimize 1 TˆxX
- Page 297 and 298: 4.2. FRAMEWORK 297asminimize ‖ỹ
- Page 299 and 300: 4.3. RANK REDUCTION 2994.3 Rank red
- Page 301 and 302: 4.3. RANK REDUCTION 301A rank-reduc
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- Page 305 and 306: 4.3. RANK REDUCTION 3054.3.3.0.1 Ex
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320 CHAPTER 4. SEMIDEFINITE PROGRAMMING5 763 841 92Figure 87: 3-lattice in R 2 , hand-drawn. Nodes 7, 8, and 9 are anchors;remaining nodes are sensors. Radio range of sensor 1 indicated by arc.range of possible distance for each measurable distance; equality constraintsexist only for anchors.Anchors are chosen so as to increase difficulty for algorithms dependenton existence of sensors in their convex hull. The challenge is to find a solutionin two dimensions close to the true sensor positions given incomplete noisyintersensor distance information.0 • • ? • ? ? • •• 0 • • ? • ? • •• • 0 • • • • • •? • • 0 ? • • • •• ? • ? 0 • • • •? • • • • 0 • • •? ? • • • • 0 ◦ ◦• • • • • • ◦ 0 ◦• • • • • • ◦ ◦ 0(747)
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