APM466H1 Lecture Notes - Lecture 9: Lagrange Multiplier, Convex Function, Entire Function
Document Summary
L( x , y , z)=f (x , y , z) h ( x , y , z)=0. Speciic example: min f ( x , y ,)=6 x 2+12 y 2 s. t. x+ y=90. L( x , y , )=6 x 2+12 y 2 ( x + y 90)=0. Example 2 (q1 from midterm last year) f 1 ( x ), f 2( x ) are convex functions. 1. f ( x )=f 1( x )+ f 2( x) is a convex funcion: at least one of f 1 ( x ), f 2( x ) are strictly convex. 3. f ( x) is strictly convex , not just in convexity deiniion. Convexity: f ( x)+(1 ) f ( y ) f ( x+(1 ) y) , [0,1] F 1( x )+( 1 ) f 1( y ) f 1 ( x+(1 ) y) F 2( x )+(1 ) f 2( y ) f 2 ( x+(1 ) y)
