Unconstrained Optimization

In this video we discuss unconstrained optimization. We will review how to find maxima and minima for 1 dimensional function by finding where the slope is equal to zero and then checking the sign of the second derivative to determine if this is a maxima or minima. We then extend this idea to higher dimensional functions. We show how to find stationary points and how to evaluate the definiteness of the Hessian matrix at these stationary point to determine if these are maxima or minima. Topics and timestamps: 0:00 – Introduction 5:31 – 1D Example 20:53 – Higher Order Extrema 25:49 – Condition for Unconstrained Optimality 50:01 – Definiteness of Hermitian Matrices 57:32 – Analytically Finding Minima 59:17 – 2D Example 1:05:43 – Practical Implementation Issues Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/main/Optimization03 Errata 46:45: This should be written as ∇^2 f (it is incorrectly written as ∇f^2) All Optimization videos in a single playlist (https://www.youtube.com/playlist?list=PLxdnSsBqCrrHo2EYb_sMctU959D-iPybT) #Optimization You can support this channel via Patreon at https://www.patreon.com/christopherwlum. Thank you for your help!