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Quantitative Finance · Glosarium

Apa itu Gradient descent, line search?

Dikenal juga sebagai: gradient descent · line search

Definition 24.1 Quantitative Methods · Bab 24 — Numerical Optimisation in Practice

Gradient descent iterates xk+1=xk−tk∇f(xk)x_{k+1} = x_k - t_k\nabla f(x_k). A line search chooses the step tkt_k along the descent direction, for instance to satisfy the Wolfe conditions: sufficient decrease, f(x+td)≤f(x)+c1t∇f(x)⊤df(x + td) \le f(x) + c_1t\nabla f(x)^\top d, and a curvature condition, ∣∇f(x+td)⊤d∣≤c2∣∇f(x)⊤d∣|\nabla f(x + td)^\top d| \le c_2|\nabla f(x)^\top d|, with 0<c1<c2<10 < c_1 < c_2 < 1.

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