Mathematical optimization | Optimization algorithms and methods

Backtracking line search

In (unconstrained) mathematical optimization, a backtracking line search is a line search method to determine the amount to move along a given search direction. Its use requires that the objective function is differentiable and that its gradient is known. The method involves starting with a relatively large estimate of the step size for movement along the line search direction, and iteratively shrinking the step size (i.e., "backtracking") until a decrease of the objective function is observed that adequately corresponds to the amount of decrease that is expected, based on the step size and the local gradient of the objective function. The stopping criterion is known as the Armijo–Goldstein condition. Backtracking line search is typically used for gradient descent (GD), but it can also be used in other contexts. For example, it can be used with Newton's method if the Hessian matrix is positive definite. (Wikipedia).

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Norm (mathematics) | Convex function | Lebesgue measure | Deep learning | Operator norm | Mathematical optimization | Subsequence | Gradient | Differentiable function | Riemann sum | Dot product | Descent direction | Morse theory | Level set | Annals of Mathematical Statistics | Learning rate | Newton's method in optimization | Wolfe conditions | Limit (mathematics) | Łojasiewicz inequality | Lipschitz continuity | Gradient descent | Critical point (mathematics) | Normal distribution | Hessian matrix | Saddle point | Compact space | Integral | Analytic function | Expected value | Line search | Stochastic gradient descent | Invertible matrix