Sentence examples for regularized problems from inspiring English sources

They determine the choice of regularization parameters and the rate at which solutions of regularized problems converge to an exact solution.

Each of these regularized problems will be obtained as a limit of these unique solutions to the regularized problems.

For the first issue, Goldstein and Osher recently introduced the split Bregman method for L 1 regularized problems.

In Section 2, we review some preliminaries concerning the variable exponent Sobolev spaces and introduce a family of regularized problems for problem (1.1).

Thus, we introduce suitable concepts of regularized semi-quasivariational optimistic bilevel problems and we study, in Banach spaces, the convergence properties of the infima and minima to these regularized problems in the presence or not of perturbations.

By virtue of the De Giorgi iteration technique, we deduce an a priori L ∞ bound for solutions to the regularized problems in Proposition 3.2; and the uniform lower bound estimate is obtained in Proposition 3.5.

The error due to regularization is then dominated by the discretization error of the regularized problem and is negligible.

Consider the regularized problem (2.1).

Proof We consider the regularized problem (2.2).

Hence, (u^{varepsilon,tau} ) is a unique solution of the regularized problem (3.1).

Next we prove that, for the regularized problem, we have stable dependence of the data.