Sentence examples for regularization sequence from inspiring English sources
where {r n } is a regularization sequence in (0, ∞).
Rockafellar's [3] proved the weak convergence of his algorithm (1.3) provided that the regularization sequence remains bounded away from zero and the error sequence satisfies the condition.
where J r A = ( I + r A ) − 1, ∀r > 0 is the resolvent of A in a Hilbert space H. Rockafellar [1] proved the weak convergence of the algorithm (1.2) provided that the regularization sequence {c n } remains bounded away from zero, and that the error sequence {e n } satisfies the condition ∑ n = 0 ∞ ∥ e n ∥ < ∞.
The proximal point algorithm generates, for any starting point (x_{0}=xin E), a sequence ({x_{n}}) by the rule x_{n+1}=J_{r_{n}}^{A}(x_{n}), (1.1) for all (ninmathbb{N}), where ({r_{n}}) is a regularization sequence of positive real numbers, (J_{r_{n}}^{A}=(I+r_{n}A)^{-1}) is the resolvent of A, and ℕ is the set of all natural numbers.
He derived a weak convergence result, which shows that for suitable choices of iterative parameters (including the regularization), the sequence of iterative solutions can converge weakly to an exact solution of the SFP.
The proof of our results is very different from that of [[17], Theorem 3.1] because our argument technique depends on Lemma 2.3, the restriction on the regularization parameter sequence { α n } and the properties of the averaged mappings P C ( I − λ n ∇ f α n ) to a great extent.
An a posteriori selection rule We construct regularization solution sequences (f^{m,delta}(x)) by the Landweber iterative method.
The main contribution is development of an architecture that combines a linear model that is fitted using ℓ1 regularization and a sequence of tanh layers.
The proposed model mainly consists of three basic components: an adaptive partition window, a nuclear norm regularization and a weighted sequence.
The forward-backward splitting method, with iteration given by y k ∈ ( I − λ k A ) − 1 x k, x k + 1 = ( I + λ k B ) − 1 y k, where { λ k } ⊆ ( 0, ∞ ) a sequence of regularization parameters.
The double backward splitting method, with iteration given by y k = ( I + λ k B ) − 1 x k, x k + 1 = ( I + λ k A ) − 1 y k, where { λ k } ⊆ ( 0, ∞ ) a sequence of regularization parameters.
