v2006.03.09 - Convex Optimization

3.1. CONVEX FUNCTION 197{a T z 1 + b 1 | a∈ R}supa T pz i + b ii{a T z 2 + b 2 | a∈ R}{a T z 3 + b 3 | a∈ R}a{a T z 4 + b 4 | a∈ R}{a T z 5 + b 5 | a∈ R}Figure 52: Pointwise supremum of convex functions remains a convexfunction. Illustrated is a supremum of affine functions in variable a evaluatedfor a particular argument a p . Topmost affine function is supremum for eachvalue of a .