Start with a trial step size and repeatedly replace by , with , until the Armijo condition holds. For a differentiable function and a descent direction, the short-step argument in the Armijo condition proves finite termination. This alone does not enforce the curvature part of the Wolfe conditions.
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Backtracking line search is an optimization technique used to determine an appropriate step size for iterative algorithms, particularly in the context of gradient-based optimization methods. The goal of the line search is to find a step size that will sufficiently decrease the objective function while ensuring that the search doesn't jump too far, which could potentially lead to instability or divergence.