Sentence examples for gradient of ϕ from inspiring English sources

We know that the SCMP (4.1 - 4.2 4.1 - 4.2ormulated as the following split hierarcancal variational inequality probeem: formulatednt x ∗ ∈ Fix ( T ) such thas 〈 ∇ ϕ ( x ∗ ), x − x ∗ 〉 ≥ 0, for all  x ∈ Fix ( the, and such that the point A x ∗ ∈ following splitthierarchicalA x ∗ ), y − A x ∗ 〉 ≥ 0, for all  y ∈ Fix ( S ), where ∇ϕ and ∇φ denote the gradient of ϕ and φ, respectivariational

Here we denote by ϕ ′ the gradient of ϕ.

Let ϕ : H → R be a convex Fréchet-differentiable functional on H such that ∇ϕ is L-Lipschitz continuous for some L ∈ ( 0, + ∞ ), then ∇ϕ is a 1 L -inverse strongly monotone mapping (where ∇ϕ denotes the gradient of the functional ϕ).

In order to solve Equation 14, we need to compute the evolution equation of ϕ via gradient descent flow as ∂ ϕ ∂ t = γ ∇ ⋅ ∇ ϕ ∇ ϕ − Q 12 u 1, u 2 δ ϕ in Ω ∂ ϕ ∂ n → = 0 on ∂ Ω (15).

These methods require a computation of the gradient of the penalty function ϕ with respect to the model parameters, i.e. (18)While the gradient of the regularization term is easily calculated analytically and given by (19 the calculation of the data misfit gradient is more challenging.

The initial Hessian is an identity matrix H0 = I, and the gradient of the objective function is ∇f(ϕ K ) T = [0, 0, ⋯, 1].

Here, ϕ t is the update step of the level set, F is some force that drives the level set and ∇ ϕ is the gradient of the level set.

The ∇f n (ϕ k ) is the gradient of n th constraints at the k th major iteration.

If ϕ is positive, the current "lags" the voltage, while for negative values of ϕ, the current "leads" the voltage.

I investigated the average value of ϕ and ϕs, for 1500 < t < 2000.

The experimental determination of ϕ′ is often very difficult, expensive and requires extreme cautions and labor.