Trust Region Methods: Coming up with the Algorithm

This lecture delves into trust region methods, focusing on the process of developing the algorithm. Starting with the shaky foundations of Newton's method, the instructor explains the core idea with nuances, emphasizing the importance of considering a subproblem at each iteration. Parameters for initialization and updating the radius are discussed, along with assessing the quality of the tentative next iterate. The lecture concludes with practical considerations and examples of successful and unsuccessful steps in the trust region subproblem.