Gradient Descent Methods: Theory and Computation

This lecture covers the principles of iterative descent methods, focusing on gradient descent for smooth convex and non-convex problems. It explains the role of computation in learning machines, the basic iterative strategy, descent directions, and the convergence rates of gradient descent. The lecture also delves into the geometric interpretation of stationarity, local minima, and challenges faced by iterative optimization algorithms. Examples such as maximum likelihood estimation, M-estimators, and ridge regression are used to illustrate the concepts discussed. The convergence rates of different sequences are explored, providing insights into the speed of convergence in optimization problems.