Descent methods and line search: Finiteness of the line search algorithm

This lecture covers the Wolfe conditions for line search algorithms, including the first and second conditions, along with the parameters involved. It explains the initialization of the line search algorithm and how to handle violations of the Wolfe conditions. The lecture delves into the properties of the algorithm and proves the finiteness of the line search parameter. By exploring the theorem on the finite number of iterations, it demonstrates that Wolfe 1 is verified for all parameters, leading to a contradiction if there were an infinite number of iterations.