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Dual method was used consistently in the preconception period by 26.8%, while 73.2% used it sometimes (non-consistently) as shown in Table 4.
Thus, the dual method provides a good approximation to the optimal solution.
We used the dual method to solve the optimization problem iteratively using the sub-gradient algorithm.
Also, the dual method can find feasible solutions for cases where the weight adjustment method cannot.
Finally, the optimal power allocation problem was solved by the Lagrangian dual method.
E. Bae et al. [8] proposed a dual method to minimize the Potts model.
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If (rhoneq1), then a linearized primal-dual method is presented in Section 6.1.
To solve the new model, we design a primal-dual method to simulate the minimization problem.
Komodakis and Pesquet [12] recently wrote a wonderful overview of recent primal-dual method for solving large-scale optimization problems.
Actually, the linearized primal-dual method (35) and (36) is a particular case where a nonsmooth proximable function is missing in [24, 25].
Bonettini et al. establish the convergence of a general primal-dual method for nonsmooth convex optimization problems, whose structure is typical in the imaging framework [13].
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com