v2010.10.26 - Convex Optimization
v2010.10.26 - Convex Optimization v2010.10.26 - Convex Optimization
34 CHAPTER 1. OVERVIEWFigure 9: Three-dimensional reconstruction of David from distance data.Figure 10: Digital Michelangelo Project, Stanford University. Measuringdistance to David by laser rangefinder. Spatial resolution is 0.29mm.
Chapter 2Convex geometryConvexity has an immensely rich structure and numerousapplications. On the other hand, almost every “convex” idea canbe explained by a two-dimensional picture.−Alexander Barvinok [26, p.vii]As convex geometry and linear algebra are inextricably bonded by asymmetry(linear inequality), we provide much background material on linear algebra(especially in the appendices) although a reader is assumed comfortable with[331] [333] [202] or any other intermediate-level text. The essential referencesto convex analysis are [199] [307]. The reader is referred to [330] [26] [371][42] [61] [304] [358] for a comprehensive treatment of convexity. There isrelatively less published pertaining to convex matrix-valued functions. [215][203,6.6] [294]2001 Jon Dattorro. co&edg version 2010.10.26. All rights reserved.citation: Dattorro, Convex Optimization & Euclidean Distance Geometry,Mεβoo Publishing USA, 2005, v2010.10.26.35
- Page 1 and 2: DATTORROCONVEXOPTIMIZATION&EUCLIDEA
- Page 3 and 4: Convex Optimization&Euclidean Dista
- Page 5 and 6: for Jennie Columba♦Antonio♦♦&
- Page 7 and 8: PreludeThe constant demands of my d
- Page 9 and 10: Convex Optimization&Euclidean Dista
- Page 11 and 12: CONVEX OPTIMIZATION & EUCLIDEAN DIS
- Page 13 and 14: List of Figures1 Overview 211 Orion
- Page 15 and 16: LIST OF FIGURES 1562 Shrouded polyh
- Page 17: LIST OF FIGURES 17130 Elliptope E 3
- Page 21 and 22: Chapter 1OverviewConvex Optimizatio
- Page 23 and 24: ˇx 4ˇx 3ˇx 2Figure 2: Applicatio
- Page 25 and 26: 25Figure 4: This coarsely discretiz
- Page 27 and 28: (biorthogonal expansion) is examine
- Page 29 and 30: 29cardinality Boolean solution to a
- Page 31 and 32: 31Figure 8: Robotic vehicles in con
- Page 33: an elaborate exposition offering in
- Page 37 and 38: 2.1. CONVEX SET 372.1.2 linear inde
- Page 39 and 40: 2.1. CONVEX SET 392.1.6 empty set v
- Page 41 and 42: 2.1. CONVEX SET 41(a)R(b)R 2(c)R 3F
- Page 43 and 44: 2.1. CONVEX SET 43where Q∈ R 3×3
- Page 45 and 46: 2.1. CONVEX SET 45Now let’s move
- Page 47 and 48: 2.1. CONVEX SET 47By additive inver
- Page 49 and 50: 2.1. CONVEX SET 49R nR mR(A T )x px
- Page 51 and 52: 2.2. VECTORIZED-MATRIX INNER PRODUC
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- Page 61 and 62: 2.3. HULLS 61Figure 20: Convex hull
- Page 63 and 64: 2.3. HULLS 63Aaffine hull (drawn tr
- Page 65 and 66: 2.3. HULLS 65subset of the affine h
- Page 67 and 68: 2.3. HULLS 672.3.2.0.2 Example. Nuc
- Page 69 and 70: 2.3. HULLS 692.3.2.0.3 Exercise. Co
- Page 71 and 72: 2.3. HULLS 71Figure 24: A simplicia
- Page 73 and 74: 2.4. HALFSPACE, HYPERPLANE 73H + =
- Page 75 and 76: 2.4. HALFSPACE, HYPERPLANE 7511−1
- Page 77 and 78: 2.4. HALFSPACE, HYPERPLANE 772.4.2.
- Page 79 and 80: 2.4. HALFSPACE, HYPERPLANE 792.4.2.
- Page 81 and 82: 2.4. HALFSPACE, HYPERPLANE 81tradit
- Page 83 and 84: 2.4. HALFSPACE, HYPERPLANE 832.4.2.
Chapter 2<strong>Convex</strong> geometry<strong>Convex</strong>ity has an immensely rich structure and numerousapplications. On the other hand, almost every “convex” idea canbe explained by a two-dimensional picture.−Alexander Barvinok [26, p.vii]As convex geometry and linear algebra are inextricably bonded by asymmetry(linear inequality), we provide much background material on linear algebra(especially in the appendices) although a reader is assumed comfortable with[331] [333] [202] or any other intermediate-level text. The essential referencesto convex analysis are [199] [307]. The reader is referred to [330] [26] [371][42] [61] [304] [358] for a comprehensive treatment of convexity. There isrelatively less published pertaining to convex matrix-valued functions. [215][203,6.6] [294]2001 Jon Dattorro. co&edg version 2010.10.26. All rights reserved.citation: Dattorro, <strong>Convex</strong> <strong>Optimization</strong> & Euclidean Distance Geometry,Mεβoo Publishing USA, 2005, <strong>v2010.10.26</strong>.35
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