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Otherwise, we can, for example, round the relaxed association variables so that x ji ∈{0,1}.
A typical approach to follow in this situation is to relax the association variables so that x ji ∈[0,1], ∀i,j [12].
In order to obtain the optimum power allocation for voice users and the association variables, we employ an iterative projected gradient approach to minimize the Lagrangian.
The tight coupling of the user association variables and the content placement variables in the objective function in (18) causes the difficulties in solving the problem.
Unfortunately, the minimization of the Lagrangian w.r.t., the association variables x ji, and the voice powers (check {p}_{ji}) cannot be obtained by differentiating the Lagrangian as they appear through linear terms.
For the association variables, the gradient is given by begin{array}{*{20}l} t_{ji} & triangleq nabla_{x_{ji}}mathcal{L}left {textbf{p}},, check{textbf{p}},, textbf{n},, textbf{x}, boldsymbolPsiright) & = beta_{j} - xi_{ji}bar{P}^{i}_{text{BS}}(C_{i}) - pi_{ji}n^{(i)}_{D}, quad forall jinmathcal{U}_{T},forall i inmathcal{B}, end{array} (17).
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In addition, its association variable corresponding to cell (i^{ast }_{k^{S }}) is updated as follows.
Equivalently, user k § 's association variable corresponding to cell i is updated as follows.
Here, the Bernoulli association variable C has been introduced to represent the uncertain structure: whether the multisensory probe observations have a common source or not.
We did not attempt to infer an individual-level association of variables from an association demonstrated only for aggregated variables.
Structure coefficients are measures of association between variables.
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