Consider two functions f(x, y) = (x - y) + xy f2(x, y) = (1-(y -...

   

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Consider two functions f₁(x, y) = (x - y)² + xy f2(x, y) = (1-(y - 4))² +35((x+6) - (y-4)²) ² (a) Run gradient descent on fi with starting point (x, y) = (2,3), T = 20 steps and y = .05. Report the function value at the end of each step (b) Run gradient descent on f2 with starting point (x, y) = = .0015. Report the function value at the end of each step (0,2), T = 100 steps and (c) Run any variant of gradient descent you want for f₁. Try to get the smallest function value after T = 20 steps (d) Run any variant of gradient descent you want for f2. Try to get the smallest function value after T = 100 steps [+5 points] If any students do significantly better than the rest of the class on f2 in part (b), we will award up to 5 extra credit points. To obtain extra points, a detailed description of how the gradient descent is performed is required. Consider two functions f₁(x, y) = (x - y)² + xy f2(x, y) = (1-(y - 4))² +35((x+6) - (y-4)²) ² (a) Run gradient descent on fi with starting point (x, y) = (2,3), T = 20 steps and y = .05. Report the function value at the end of each step (b) Run gradient descent on f2 with starting point (x, y) = = .0015. Report the function value at the end of each step (0,2), T = 100 steps and (c) Run any variant of gradient descent you want for f₁. Try to get the smallest function value after T = 20 steps (d) Run any variant of gradient descent you want for f2. Try to get the smallest function value after T = 100 steps [+5 points] If any students do significantly better than the rest of the class on f2 in part (b), we will award up to 5 extra credit points. To obtain extra points, a detailed description of how the gradient descent is performed is required.

Answer rating: 100% (QA)

a Gradient descent on f1 with starting point xy 23 T20 steps and 05 We have the following partial derivatives of f1 with respect to x and y f1x 2xy y f1y 2yx x Using the starting point 23 we have f1x ... View the full answer