With the vigorous development of artificial intelligence technology, various engineering technology applications have been implemented one after another. The gradient descent method plays an important role in solving optimization problems, due to its simple structure, good stability, and easy implementation. However, multinode machine learning system, gradients usually need be shared, which wil...

Sparse learning based feature selection has been widely investigated in recent years. In this study, we focus on the l2,0-norm selection, which is effective for exact top-k but challenging to optimize. To solve general constrained problems, novelly develop a parameter-free optimization framework coordinate descend (CD) method, termed CD-LSR. Specifically, devise skillful conversion from origina...

The paper is devoted to the classical variational problem with a nonsmooth integrand of functional be minimized. supposed subdifferentiable. Under some natural conditions subdifferentiability considered proved. finding subdifferential descent direction solved and method applied solve original problem. algorithm developed demonstrated by examples.

2 Method 1 2.1 Optical Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Lucas Kanade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3 Gradient Descent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Conjugate Gradient Descent . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.5 Newton’s Method . . . . . . ...

In recent years, attention has been focused on the relationship between black box optimization and reinforcement learning. Black box optimization is a framework for the problem of finding the input that optimizes the output represented by an unknown function. Reinforcement learning, by contrast, is a framework for finding a policy to optimize the expected cumulative reward from trial and error....

If one assumes k to have a discrete valuation, then descent theory for coherent sheaves is an old result of Gabber. Gabber’s method was extended to the general case by Bosch and Görtz [BG]. Our method is rather different from theirs (though both approaches do use Raynaud’s theory of formal models [BL1], [BL2], we use less of this theory). We think that our approach may be of independent interes...

The celebrated Nesterov’s accelerated gradient method offers great speed-ups compared to the classical gradient descend method as it attains the optimal first-order oracle complexity for smooth convex optimization. On the other hand, the popular AdaGrad algorithm competes with mirror descent under the best regularizer by adaptively scaling the gradient. Recently, it has been shown that the acce...