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The output signal is then filtered by a dual variable filter (Kemo, model VBF4, Beckenham, UK) and sent to an oscilloscope, a X-Y recorder or a microcomputer.
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Introduce a dual variable λ≥0 for the constraint (12b).
where, and is a dual variable associated with the power constraint in (29).
In fact, the former are just a dual variables formulation of the latter.
Let v n = (1 / ρ)u n (i.e., v n is a scaled dual variable).
A low-complexity algorithm was proposed in [11] to solve the dual problem by updating dual variables through a gradient descent.
Particular important pairs of Lagrangian maximizers are those associated with a given optimal dual variable Λ∗.
If the solution is not feasible either directly or by recomputing the power allocation for the SDMA set assignment found in the dual problem, the algorithm performs a search by increasing the dual variables associated to the users whose QoS constraints are not met until a new SDMA set assignment is found.
By introducing dual variables and applying the variational principle, the canonical equations of Hamiltonian system are constructed.
The calculation method of electric nodal prices can be found in [32], while the natural gas nodal prices are determined by the dual variables of the equality constraint (36) at the optimal solution point of the optimization model.
To make the above problem tractable, (57), (63) and (69) must be converted into corresponding dual problems (60), (66) and (72) by introducing dual variables λ c t, π c1 t+, π c1 t−, λ h t, π h1 t+, π h1 t−, λ nl t, π l1 t+, π l1 t−, π pv2 t+, and π pv2 t−.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com