Sentence examples for by the dual method from inspiring English sources

Natural examples of the second kind of independence are provided by the dual method of inner and outer models.

In our precedent work [22], the optimal order of convergence (3.9986) was obtained by the dual method.

However, if it is small enough, we can use the solution provided by the dual method as a useful benchmark to check the accuracy of heuristic methods.

The variables of problem (1) are rk,n, pk,n and S k, k = 1, …, K, n = 1, …, N. The dual optimum of (1) can be obtained by the dual method [10].

Based on the SC assignment (left ({delta _{k}^{l}}right)^) determined through solving the subproblem (mathcal {OP}_{2a}), the subproblem (mathcal {OP}_{2b}) can be solved by the dual method.

It is clear that, no matter the noise level is light or heavy, the restored results by our method are much better than those by the dual method, especially in the contours and details, such as the hair and the hat. Figure 5 3-D orimagel image.

Comparison results show again that the contours and the details such as the girl's hair, mole, nose and teeth are recovered more clearly by our new method than the dual method.

This can be achieved by abstinence, consistent condom use, or the dual methods of condoms plus an effective non-barrier contraceptive.

Then by the Lagrangian dual method, the closed-form expressions of the optimal power and time allocation strategy have been derived given the underlying statistical delay QoS constraint.

First, we transform Eq. (10) to a convex problem by changing the optimized variable and ignoring some constraints and solve it by the Lagrange dual method.

Finally, the optimal power allocation problem was solved by the Lagrangian dual method.