Line search

In optimization, line search is a basic iterative approach to find a local minimum ${\displaystyle \mathbf {x} ^{*}}$ of an objective function ${\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} }$. It first finds a descent direction along which the objective function ${\displaystyle f}$ will be reduced, and then computes a step size that determines how far ${\displaystyle \mathbf {x} }$ should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly or inexactly.