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Dual methods based on sequential approximations are usually employed for solving topology optimization problems.
Project PROTECT compared two approaches to promote the use of dual methods of contraception among high-risk women.
The numerical resolution of a nonlinear programming problem is standard, by gradient methods, penalization, quasi-Newton, dual methods, etc. (see, e.g., [9, 50, 57, 81]).
With two adjustable parameters per binary, it can represent low-pressure vapor liquid equilibria as well or better than dual methods.
This model applies a single equation to both phases and necessitates only a fraction of the input information required by dual methods.
This can be achieved by abstinence, consistent condom use, or the dual methods of condoms plus an effective non-barrier contraceptive.
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Also, the dual method can find feasible solutions for cases where the weight adjustment method cannot.
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.
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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