We analyze the eddy-current approximation of Maxwell's equations to describe the electric field for heterogeneous, isotropic magnetic materials.
Since the end point of each line search is the current approximation to the point of maximal quality, experts might advantageously use feedback on search progress to use their time even more efficiently.
Let x k be a current approximation to the solution of EP ( f, C ). First, we compute y k = argmin { f ( x k, y ) + β 2 ∥ y − x k ∥ 2 ∣ y ∈ C } (2.1).
Applying this idea and interior proximal function technique D to the equilibrium problem EP f, C), we obtain the solution scheme: Let x k be a current approximation to the solution of EP f, C).
As an illustration, relatively current approximations for the effective yield curvature of reinforced concrete (RC) members and steel members are (Priestley et al. 2007) given in Table 1.
At stage k, it identifies the dictionary atom that best correlates with the residual and then adds to the current approximation a scalar multiple of that atom, such that x ^ ( k ) ( m ) = x ^ ( k - 1 ) ( m ) + α k ϕ k ( m ) (19) R ( k ) ( m ) = x ( m ) - x ^ ( k ) ( m ) (20).
After obtaining the identified support-set W 1, we unite the support-set of current approximation ({{{{overset smile {boldsymbol {Psi }} }}}^{left ({k - 1} right)}}) to construct a merger support-set T in the kth iteration, i.e., {mathrm{T}} leftarrow {text{supp}}left({{{{oversetsmile{boldsymbol{Psi}} }}}^{left {k - 1} right)}} right) bigcup {{mathbf{W}}_{1}}.
Then, calculate the residual, r t, of the current approximation.
An EP update of the current approximation Q focuses on a site j ∈ {1,..., N}, constructing the distribution P ^ j (a ) ∝ Q(a ) t j (a j )/ t ˜ j (a j ), then adjusting b j, π j such that the new approximation Q' matches first and second order moments (mean and covariance) of P ^ j.
Current approximation x k is updated in the direction of the optimal update vector Δ k by a unit distance.
