Sentence examples for a unique solution of the regularized from inspiring English sources

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

(a) For, let be the unique solution of the regularized VIP  .

For, let be the unique solution of the regularized VIP (2.1).

By using the obtained equivalence formulations, we prove the existence of a unique solution for the regularized nonconvex variational inequalities and propose some projection iterative schemes for solving the regularized nonconvex variational inequalities.

Then we use the regularized gradient-projection composite iterative method to find a unique solution of ((A+B)^{-1}0cap U).

This equivalence and two nearly uniformly Lipschitzian mappings S i (i = 1, 2) are used to suggest and analyze a new perturbed p-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = ( S 1, S 2 ) which is the unique solution of the system of general nonlinear regularized nonconvex variational inequalities.

However, in this paper, we use the regularized gradient-projection algorithm to find the unique solution of the problems of constrained convex minimization problem and the zero points of maximal monotone operator, which also solves a certain variational inequality.

For any bi-function the associated Yosida approximation over and the corresponding regularized operator are defined as follows: (1.14). in which is the unique solution of the following problem: (1.15).

Equivalently, is the unique solution in of the regularized minimization problem: (4.5).

The regularized minimization (1.9) has a unique solution which is denoted by x α.

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