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In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum x ∗ {\displaystyle \mathbf {x} ^{*}} of an objective function f : R n → R {\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 f {\displaystyle f} will be reduced and then computes a step size that determines how far x {\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.
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