Sentence examples for dual associated from inspiring English sources

In addition, a sensitivity analysis is performed using a method that consists of transforming the data parameters into artificial variables, and using the dual associated variables.

In addition, a sensitivity analysis is performed using a method that consists of transforming the data parameters into artificial variables and using the dual associated problem.

The reduced cost of a newly found column can be computed as follows: (7) c ¯ ω = c ω − ∑ i ∈ P b i ω π i − σ, where π i denotes the dual variable associated with constraint (3) for request i, and σ the dual variable associated with constraint (4).

The KKT conditions, necessary for the optimality, are given by (31) where is the Lagrangian dual matrix associated to the positive semidefiniteness constraints for and is the Lagrangian dual variable associated to the total power constraint.

where is the Lagrangian dual matrix associated to the positive semidefiniteness constraint of for and is the Lagrangian dual variable associated to the total power constraint.

It can be easily shown that the KKT conditions are given by (29) where is the Lagrangian dual matrix associated to the positive semidefiniteness constraint of for and is the Lagrangian dual variable associated to the total power constraint.

(6) The second term in (6) originates from the linear dependence of dual areas corresponding to the cell edges perpendicular to the thickness, whereas the third term originates from dual areas associated to cell edges tangential to the thickness orientation.

The second term originates from the linear dependence of dual areas corresponding to the cell edges perpendicular to the thickness orientation, whereas the third term originates from dual areas associated to cell edges tangential to the thickness orientation [11].

Fortunately, if we come back to the problem definition in (2), we notice that there is a dependence between the dual variable associated to the constraint h j (x j )≤ y j, i.e., λ j, and the dual variable associated to the constraint ∑ j = 1 J y j ≤ C, i.e., μ (in terms of the proposed algorithm, ŷ j k, λ ̂ j k and μ k play the role of y j, λ j and μ, respectively).

where β and θ are the Lagrangian multipliers (dual variables) related to the power constraints at the source and the relay, and λ and μ represent the dual variables associated to the interference constraints.

Let denote the dual variable associated with node.