Line search

In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum ${\displaystyle \mathbf {x} ^{*}}$ of an objective function ${\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} }$. The other approach is trust region.

The line search approach 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, Newton's method and Quasi-Newton method. The step size can be determined either exactly or inexactly.

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