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Suppose f(x) = x². You want to find a point at which this function is minimized %3D using the gradient descent algorithm. Your xo = -1 and 1 = 1. After how many steps, you can find a point at which f is minimized?e

Suppose f(x) = x². You want to find a point at which this function is minimized %3D using the gradient descent algorithm. Your xo = -1 and 1 = 1. After how many steps, you can find a point at which f is minimized?e

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Gradient descent is an optimization algorithm to find a point at which a differentiable function is maximized (or minimized depending on what you want to do). (Rigorously, speaking it is a local maximum or local minimum, but you can ignore the distinction between global and local for the exam.) Gradient descent algorithm is an iterative process. Here is how it works. First you choose 1 and an initial point xo. You will find the next x, namely x1, by calculating xo – af' (xo) where f' is the first order derivative of f for which you want to find a maximum or minimum. In general, for any n, you get xn+1 = Xn – af'(xn). This iteration - stops when xn+1 and xn are close enough. - Suppose f (x) = x?. You want to find a point at which this function is minimized using the gradient descent algorithm. Your xo = -1 and 2 = 1. After how many steps, you can find a point at which f is minimized?e
Transcribed Image Text:Gradient descent is an optimization algorithm to find a point at which a differentiable function is maximized (or minimized depending on what you want to do). (Rigorously, speaking it is a local maximum or local minimum, but you can ignore the distinction between global and local for the exam.) Gradient descent algorithm is an iterative process. Here is how it works. First you choose 1 and an initial point xo. You will find the next x, namely x1, by calculating xo – af' (xo) where f' is the first order derivative of f for which you want to find a maximum or minimum. In general, for any n, you get xn+1 = Xn – af'(xn). This iteration - stops when xn+1 and xn are close enough. - Suppose f (x) = x?. You want to find a point at which this function is minimized using the gradient descent algorithm. Your xo = -1 and 2 = 1. After how many steps, you can find a point at which f is minimized?e
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