Let be the optimized value which minimizes the term from (6), then: (7).
It is evident from Equation 20 that in order to maximize R0, one has to minimize the term F ( A ) = ∑ Y ∑ Z ∏ j = 1 N 1 1 + G j σ 2 mn.
Minimizing Equation (1) is equivalent to minimizing the first term while maximizing the second term.
In (28), the proposed beamformer exploits the knowledge of the local channels to find the best trade-off to optimize the SINR criterion between maximizing the energy of the useful information (transmit-MRC), i.e., the terms at the numerator, and minimizing the interference terms (ZF), i.e., the terms at the denominator.
Similarly as before, we know that the necessary condition of minimizing the ith term of the last line in (51) is that (w g ∘ z i ) g ) is parallel to (w g ∘(x i ) g ).
From the deduction of the two-dimensional shrinkage formula (7) in Section 2.1, we know that the necessary condition of minimizing the ith term of the last line in (14) is that (z i ) g is parallel to (x i ) g.
A potential risk of regularization, as always with multi-objective optimization, is that for a low λ the regularization term has no effect, whereas for a large λ the parameter estimation algorithm might focus on minimizing the regularization term while describing the experimental data inaccurately.
Ma et al. performed the variational optimization by minimizing the constraint term on the reflectance component using l 1-norm [18].
In other words, choosing this transformation will minimize ∥wk,n,s∥ so that it is minimizing the power term in the objective function in (29).
Observe that, as μ2 is a constant, minimizing (V[{mathcal {F}}^{1}]) means minimizing the first term of the last equality in Eq. 41.
