Descent methods and line search: First Wolfe condition

This lecture focuses on identifying a step along a descent direction to generate a new iterate, characterizing a good step with the First Wolfe condition. The condition ensures that the decrease in the objective function is proportional to the step length, with the proportionality factor gamma. The lecture illustrates the condition with examples, emphasizing the importance of choosing an appropriate value for gamma based on the local slope of the function. The concept of beta_1, strictly between zero and one, is introduced to define the requirement for the decrease of the function, depending on the directional derivative. The lecture concludes by demonstrating how different values of beta_1 impact the acceptability of steps, highlighting the significance of selecting a value close to zero for practical purposes.