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Line search

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} o mathbb {R} } . The other approach is trust region. 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} o 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, Newton's method and quasi-Newton method. The step size can be determined either exactly or inexactly.

[ "Convergence (routing)", "line search algorithm", "Newton line", "Backtracking line search", "spectral gradient method" ]
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