A line search chooses a positive step size along a search vector , updating to . For a differentiable function , a descent direction makes sufficiently short steps decrease the objective function; an Armijo condition quantifies the decrease, while the Wolfe conditions also prevent accepting an unnecessarily short step.
Line search is an optimization technique used to find a minimum (or maximum) of a function along a specified direction. It is commonly employed in gradient-based optimization algorithms, especially in the context of iterative methods like gradient descent, where the goal is to minimize a differentiable function. ### Key Components of Line Search: 1. **Objective Function**: The function \( f(x) \) that we want to minimize.
New to topics? Read the docs here!