Optimization Basics: Unconstrained Optimization and Gradient Descent

This lecture introduces the concept of optimization, emphasizing its omnipresence in various fields. It covers unconstrained optimization, distinguishing between global and local minima. The instructor explains the algorithm overview and the role of gradients in finding the optimal solution. The lecture delves into the gradient descent method, detailing how it iteratively approaches the minimum of an objective function. It discusses the gradient as the best linear approximation and its significance in determining the steepest ascent direction. The presentation concludes with strategies for determining the step length in optimization problems, highlighting the basic gradient descent algorithm.