This preview shows page 1. Sign up to view the full content.
Unformatted text preview: S and c [0 , 1] we have that (1) f ( cx + (1-c ) y ) cf ( x ) + (1-c ) f ( y ) (2) g ( cx + (1-c ) y ) cg ( x ) + (1-c ) g ( y ) Adding (1) and (2) yields h ( cx + (1-c ) y ) ch ( x ) + (1-c ) h ( y ) which shows that h is also a convex function. 13. Since f is convex we know that for 0 k 1 (1) f ( kx + (1-k ) y ) kf ( x ) + (1-k ) f ( y ). Multiplying both sides of (1) by c 0 shows that g is also a convex function. Similarly, multiplyng both sides of (1) by c 0 shows that g is a concave function....
View Full Document
- Spring '07
- Operations Research