v2010.10.26 - Convex Optimization
v2010.10.26 - Convex Optimization v2010.10.26 - Convex Optimization
98 CHAPTER 2. CONVEX GEOMETRY0Figure 35: Boundary of a convex cone in R 2 is a nonconvex cone; a pair ofrays emanating from the origin.XXFigure 36: Union of two pointed closed convex cones is nonconvex cone X .
2.7. CONES 99XXFigure 37: Truncated nonconvex cone X = {x ∈ R 2 | x 1 ≥ x 2 , x 1 x 2 ≥ 0}.Boundary is also a cone. [250,2.4] Cartesian axes drawn for reference. Eachhalf (about the origin) is itself a convex cone.X0Figure 38: Nonconvex cone X drawn truncated in R 2 . Boundary is also acone. [250,2.4] Cone exterior is convex cone.
- 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
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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
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- Page 71 and 72: 2.3. HULLS 71Figure 24: A simplicia
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- Page 81 and 82: 2.4. HALFSPACE, HYPERPLANE 81tradit
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98 CHAPTER 2. CONVEX GEOMETRY0Figure 35: Boundary of a convex cone in R 2 is a nonconvex cone; a pair ofrays emanating from the origin.XXFigure 36: Union of two pointed closed convex cones is nonconvex cone X .
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