v2009.01.01 - Convex Optimization

212 CHAPTER 3. GEOMETRY OF CONVEX FUNCTIONS
{a T z 1 + b 1 | a∈ R}
supa T pz i + b i
i
{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 64: Pointwise supremum of convex functions remains a convex
function. Illustrated is a supremum of affine functions in variable a evaluated
for a particular argument a p . Topmost affine function is supremum for each
value of a .