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Gradient descent with momentum remembers the solution update at each iteration, and determines the next update as a linear combination of the gradient and the previous update. For unconstrained quadratic minimization, a theoretical convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate ...
If used in gradient descent methods, random preconditioning can be viewed as an implementation of stochastic gradient descent and can lead to faster convergence, compared to fixed preconditioning, since it breaks the asymptotic "zig-zag" pattern of the gradient descent.
The LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be slower than the GNA.
In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete:
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.
Choosing a proportionality constant and eliminating the minus sign to enable us to move the weight in the negative direction of the gradient to minimize error, we arrive at our target equation: = ′ ().
Coordinate descent does a line search along one coordinate direction at the current point in each iteration. Some versions of coordinate descent randomly pick a different coordinate direction each iteration. Random-restart hill climbing is a meta-algorithm built on top of the hill climbing algorithm. It is also known as Shotgun hill climbing.
steepest descent (with variable learning rate and momentum, resilient backpropagation); quasi-Newton (Broyden–Fletcher–Goldfarb–Shanno, one step secant); Levenberg–Marquardt and conjugate gradient (Fletcher–Reeves update, Polak–Ribiére update, Powell–Beale restart, scaled conjugate gradient). [4]