Motivation-"real world problem Then we minimize E(C, h)=argmin(1-h)E, (x)+E, (x) x∈R >High dimension non-linear problem Conjugate gradient method is maybe the most popular optimization technique based on what we'll see here
Motivation- “real world” problem ØThen we minimize: ØHigh dimension non-linear problem. ØConjugate gradient method is maybe the most popular optimization technique based on what we’ll see here. 3 ( , ) arg min 1 ( ) ( ) n s r x E C E x E x
Directional derivatives first. the one dimension derivative .1 -0.05 d -.1 40.15 dx
Directional Derivatives: first, the one dimension derivative:
Directional derivatives Along the axes of(, y) y of(x, y) oX
x f x y ( , ) y f x y ( , ) Directional Derivatives : Along the Axes…
Directional derivatives In general direction v∈R21 of(x, y OV
v f x y ( , ) 2 v R v 1 Directional Derivatives : In general direction…