where λ is a positive regularization coefficient.
where α is a positive regularization parameter.
The updating is done through a positive regularization parameter and a hinge loss function.
where is a positive constant called the regularization parameter and called -norm SVM loss.
Gradient-based optimization is then used to minimize the following function, equal to a penalized log-likelihood, (5) F = β E D D w, M + α E W w M, where E W (w |M) is the sum of squares of network weights, M is the ANN architecture, and α and β are positive regularization parameters that must be estimated.
Here, (varepsilon^{2}) is the positive regularization parameter, which is used to characterize the weight of the prior information constraint in the proposed algorithm.
Moreover, Rockafellar [2] has given a more practical method which is an inexact variant of the method: x_{n}+e_{n}ni x_{n+1}+r_{n}Ax_{n+1}, (1.3) for all (ninmathbb{N}), where ({e_{n}}) is regarded as an error sequence and ({r_{n}}) is a sequence of positive regularization parameters.
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.
λ is a regularization parameter, and f is a regularization function depending on the regularization method such as Tikhonov regularization method, the total variation method, etc [ 25].
where α > 0 is a small regularization parameter.
