v2010.10.26 - Convex Optimization

80 CHAPTER 2. CONVEX GEOMETRYCH −H +0 > κ 3 > κ 2 > κ 1{z ∈ R 2 | a T z = κ 1 }a{z ∈ R 2 | a T z = κ 2 }{z ∈ R 2 | a T z = κ 3 }Figure 28: (confer Figure 73) Each linear contour, of equal inner product invector z with normal a , represents i th hyperplane in R 2 parametrized byscalar κ i . Inner product κ i increases in direction of normal a . i th linesegment {z ∈ C | a T z = κ i } in convex set C ⊂ R 2 represents intersection withhyperplane. (Cartesian axes drawn for reference.)