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In this case, we can transform the constraint into a very simple algebra equation that can be explicitly implemented via direct projection approach without re-initialization.
In order to circumvent numerical difficulties in solving the nested double-loop optimization problem, a performance measure-based approach is employed to transform the constraint on the reliability index into one on the concerned performance.
To transform the constraint in (13), according to [22] an equation is obtained which models the relationship between the scheduled data rate of the user i and its traffic characteristic (τ i λ i ).
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By transforming the constraints containing fuzzy variables into their equivalent forms, the chance constraints are converted into deterministic constraints which consider the fuzzy risks (or reliability) as well.
Bernstein's approximation is applied to transform the chance constraint into a convex constraint, and the Lagrangian dual algorithm is used to solve the convex power optimization problem.
Besides, there is a method to deal with the first one index in [2]: a weighting matrix is introduced to transform the (H_) constraint into a (H_{infty}) constraint.
Furthermore, the problem is reformulated by introducing an extra decision vector to transform the original constraints into linear constraints, and then, a two-phase method is presented to solve the problem efficiently.
In this study, we formulate the network design problem as a single-level optimization problem with equilibrium constraints, and then we transform the equilibrium constraints into a set of mixed-integer constraints and linearize the travel time function.
To solve the resultant design problem, a Bernstein-type inequality for stochastic processes of quadratic forms of Gaussian variables is employed to transform the probabilistic constraint to a deterministic form.
An algorithm is developed to transform the information constraints throughout the ICN into a Petri net model.
To optimize the diagonal vector, the Bernstein-type inequality is utilized to transform the probabilistic constraints into closed-form expressions, making the problem easy to tackle.
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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