MATH 1XX3 Lecture Notes - Lecture 31: Differentiable Function, Gradient Descent, Level Set

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Setup : suppose we are on a hill defined by flx , y ) : 4 - x2 - 2y2. 1) we can move in any direction described by the unit. Directional derivative (cid:574) do flx , y ) = fxa + fyb = of . In our example , in direction t= ( a. , -4g > so at the point p= ( 1,1 , Djfal ) = pfa , 1) . j. This gives direction of t the change inheight starting at point (l , l ) and moving in the. Ijihi cos o to find the steepest ascent ? ie how do we maximize. This is maximized when cos 0=1 (cid:12200) > 0=0. 0 is maximized when 0 points in the same direction as. In our example : tflx , g) = ( - 2x , -4g > Jf 1 1,1 ) = ( -2 ,

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