v2007.09.13 - Convex Optimization
v2007.09.13 - Convex Optimization v2007.09.13 - Convex Optimization
82 CHAPTER 2. CONVEX GEOMETRYX(a)00(b)XFigure 22: (a) Two-dimensional nonconvex cone drawn truncated. Boundaryof this cone is itself a cone. Each polar half is itself a convex cone. (b) Thisconvex cone (drawn truncated) is a line through the origin in any dimension.It has no relative boundary, while its relative interior comprises entire line.0Figure 23: This nonconvex cone in R 2 is a pair of lines through the origin.[181,2.4]
2.7. CONES 830Figure 24: Boundary of a convex cone in R 2 is a nonconvex cone; a pair ofrays emanating from the origin.X0Figure 25: Nonconvex cone X drawn truncated in R 2 . Boundary is also acone. [181,2.4] Cone exterior is convex cone.
- Page 31 and 32: 31appendicesProvided so as to be mo
- Page 33 and 34: Chapter 2Convex geometryConvexity h
- Page 35 and 36: 2.1. CONVEX SET 35Figure 9: A slab
- Page 37 and 38: 2.1. CONVEX SET 372.1.6 empty set v
- Page 39 and 40: 2.1. CONVEX SET 392.1.7.1 Line inte
- Page 41 and 42: 2.1. CONVEX SET 41(a)R 2(b)R 3(c)(d
- Page 43 and 44: 2.1. CONVEX SET 43This theorem in c
- Page 45 and 46: 2.2. VECTORIZED-MATRIX INNER PRODUC
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- Page 53 and 54: 2.3. HULLS 53Figure 12: Convex hull
- Page 55 and 56: 2.3. HULLS 55Aaffine hull (drawn tr
- Page 57 and 58: 2.3. HULLS 57The union of relative
- Page 59 and 60: 2.4. HALFSPACE, HYPERPLANE 59of dim
- Page 61 and 62: 2.4. HALFSPACE, HYPERPLANE 61H +ay
- Page 63 and 64: 2.4. HALFSPACE, HYPERPLANE 63Inters
- Page 65 and 66: 2.4. HALFSPACE, HYPERPLANE 65Conver
- Page 67 and 68: 2.4. HALFSPACE, HYPERPLANE 67A 1A 2
- Page 69 and 70: 2.4. HALFSPACE, HYPERPLANE 69tradit
- Page 71 and 72: 2.4. HALFSPACE, HYPERPLANE 71There
- Page 73 and 74: 2.5. SUBSPACE REPRESENTATIONS 732.5
- Page 75 and 76: 2.5. SUBSPACE REPRESENTATIONS 752.5
- Page 77 and 78: 2.6. EXTREME, EXPOSED 77In other wo
- Page 79 and 80: 2.6. EXTREME, EXPOSED 792.6.1 Expos
- Page 81: 2.7. CONES 812.6.1.3.1 Definition.
- Page 85 and 86: 2.7. CONES 852.7.2 Convex coneWe ca
- Page 87 and 88: 2.7. CONES 87Thus the simplest and
- Page 89 and 90: 2.7. CONES 89nomenclature generaliz
- Page 91 and 92: 2.8. CONE BOUNDARY 91Proper cone {0
- Page 93 and 94: 2.8. CONE BOUNDARY 93the same extre
- 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
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- Page 108 and 109: 108 CHAPTER 2. CONVEX GEOMETRY2.9.2
- Page 110: 110 CHAPTER 2. CONVEX GEOMETRYA con
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- Page 121 and 122: 2.10. CONIC INDEPENDENCE (C.I.) 121
- Page 123 and 124: 2.10. CONIC INDEPENDENCE (C.I.) 123
- Page 125 and 126: 2.10. CONIC INDEPENDENCE (C.I.) 125
- Page 127 and 128: 2.12. CONVEX POLYHEDRA 127It follow
- Page 129 and 130: 2.12. CONVEX POLYHEDRA 129Coefficie
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2.7. CONES 830Figure 24: Boundary of a convex cone in R 2 is a nonconvex cone; a pair ofrays emanating from the origin.X0Figure 25: Nonconvex cone X drawn truncated in R 2 . Boundary is also acone. [181,2.4] Cone exterior is convex cone.
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