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In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point.
The optimized gradient method (OGM) [26] reduces that constant by a factor of two and is an optimal first-order method for large-scale problems. [27] For constrained or non-smooth problems, Nesterov's FGM is called the fast proximal gradient method (FPGM), an acceleration of the proximal gradient method.
[1] [2] When a decision tree is the weak learner, the resulting algorithm is called gradient-boosted trees; it usually outperforms random forest. [1] As with other boosting methods, a gradient-boosted trees model is built in stages, but it generalizes the other methods by allowing optimization of an arbitrary differentiable loss function.
The conjugate gradient method can be derived from several different perspectives, including specialization of the conjugate direction method for optimization, and variation of the Arnoldi/Lanczos iteration for eigenvalue problems. Despite differences in their approaches, these derivations share a common topic—proving the orthogonality of the ...
Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near ...
Specific approaches include the projected gradient descent methods, [29] [30] the active set method, [6] [31] the optimal gradient method, [32] and the block principal pivoting method [33] among several others. [34] Current algorithms are sub-optimal in that they only guarantee finding a local minimum, rather than a global minimum of the cost ...
Proximal gradient methods provide a general framework which is applicable to a wide variety of problems in statistical learning theory. Certain problems in learning can often involve data which has additional structure that is known a priori. In the past several years there have been new developments which incorporate information about group ...
The theory of stationary iterative methods was solidly established with the work of D.M. Young starting in the 1950s. The conjugate gradient method was also invented in the 1950s, with independent developments by Cornelius Lanczos, Magnus Hestenes and Eduard Stiefel, but its nature and