Newton's Method

Preliminaries ‘steepest descent algorithm’ Linear Algebra Calculus 1,2 Newton’s Method1 Taylor series gives us the conditions for minimum points based on both first-order items and the second-order item. And first-order item approximation of a performance index function produced a powerful algorithm for locating the minimum points which we call ‘steepest descent algorithm’. Now we want to have an insight into the second-order approximation of a function to find out whether there is an algorithm that can also work as a guide to the minimum points....

December 21, 2019 · (Last Modification: May 3, 2022) · Anthony Tan

Steepest Descent Method

Preliminaries ‘An Introduction to Performance Optimization’ Linear algebra Calculus 1,2 Direction Based Algorithm and a Variation1 This post describes a direction searching algorithm(\(\mathbf{x}_{k}\)). And its variation gives a way to estimate step length (\(\alpha_k\)). Steepest Descent To find the minimum points of a performance index by an iterative algorithm, we want to decrease the value of the performance index step by step which looks like going down from the top of the hill....

December 20, 2019 · (Last Modification: May 3, 2022) · Anthony Tan