Since MSE min does not depend on g s, the MSE is minimized by minimizing the term MSE excess which can be controlled through the path selection vector g s.
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.
(12 The algorithm minimizes the left term in Eq. (12) with respect to the attenuation.
TransCanada, Canadian Prime Minister Stephen Harper, big oil companies and many Washington politicians are engaged in a superficial cost/benefit analysis that emphasizes the short-term economic costs and benefits of the Keystone XL pipeline, but minimizes the long-term environmental consequences.
The model minimizes the long-term costs of infrastructure investments and the operational costs of generation.
Minimizing Equation (1) is equivalent to minimizing the first term while maximizing the second term.
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.
Since the second constraint is only related to T ab, and the last constraint is only related to T ba, the joint optimization problem can be decoupled into two subproblems, i.e., optimizing T ab to minimize the first term in objective function with the constraint T ab ≥ Tmin1, and optimizing T ba to minimize the second term in objective function with the constraint T ba ≥ Tmin2.
