Sentence examples for projection of the gradient from inspiring English sources

If f is the restriction of a globally defined function f ̂ to M, the Riemannian gradient is just the orthogonal projection of the gradient of f ̂ to the tangent space, i.e. grad f ( x ) = π x ∇ f ̂ ( x ), (35).

In our work, an iterative gradient approach is used for revenue maximization in (20), where a successive projection of the revenue gradient is performed to converge to 0. We use a step-size factor φ to scale the projected spectrum size changes ΔO = (ΔS1, ΔS2,..., ΔS W ) at each iteration step to improve the convergence.

The gradients g (p e ) are obtained as the projections of the gradients g ˆ (p e ) into the normal plane of the curve p e.

The natural or Riemannian gradient of a function that is the restriction of some globally defined function to a sub-manifold is simply the orthogonal projection of the Euclidean gradient onto the corresponding tangent space.

A natural derivative ∂ ˜ x i of a function f (x ) defined on the unit sphere is the projection of the ordinary gradient ∇ x in R 2 N onto the tangent space of the sphere (9) ∂ ˜ x i f (x ) = [ (1 − x x T ) ∇ x f (x ) ] i.

by means of the gradient projection method.

Each iteration of the gradient projection method produces a valid solution.

Using an extension of the gradient projection method, an alternating minimization algorithm is employed to solve the corresponding energy function.

then the CQ algorithm (1.3) comes immediately as a special case of the gradient projection algorithm (GPA).

then the CQ algorithm (1.2) comes immediately as a special case of the gradient projection algorithm (GPA)(For more details about the GPA, the reader is referred to [18]).

An interesting problem is whether a global convergence (if not for all starting points, then at least for most of them) of the gradient projection algorithm can be achieved by requiring that for some sufficiently large constant.