Search results
Results From The WOW.Com Content Network
The number of gradient descent iterations is commonly proportional to the spectral condition number of the system matrix (the ratio of the maximum to minimum eigenvalues of ), while the convergence of conjugate gradient method is typically determined by a square root of the condition number, i.e., is much faster.
As observed above, is the negative gradient of at , so the gradient descent method would require to move in the direction r k. Here, however, we insist that the directions must be conjugate to each other. A practical way to enforce this is by requiring that the next search direction be built out of the current residual and all previous search ...
The first widely used algorithm for solving this problem is an active-set method published by ... in MATLAB as the ... 's gradient descent method ...
Stochastic gradient descent competes with the L-BFGS algorithm, [citation needed] which is also widely used. Stochastic gradient descent has been used since at least 1960 for training linear regression models, originally under the name ADALINE. [25] Another stochastic gradient descent algorithm is the least mean squares (LMS) adaptive filter.
Another way is the so-called adaptive standard GD or SGD, some representatives are Adam, Adadelta, RMSProp and so on, see the article on Stochastic gradient descent. In adaptive standard GD or SGD, learning rates are allowed to vary at each iterate step n, but in a different manner from Backtracking line search for gradient descent.
Whereas linear conjugate gradient seeks a solution to the linear equation =, the nonlinear conjugate gradient method is generally used to find the local minimum of a nonlinear function using its gradient alone. It works when the function is approximately quadratic near the minimum, which is the case when the function is twice differentiable at ...
The line-search method first finds a descent direction along which the objective function will be reduced, and then computes a step size that determines how far 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 ...
In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. [1] Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information.