(I'll note that while it is natural and effective to use calculus to solve the maximization problem in the induction step, it can be done without calculus by using substitution to put the function to be maximized in the form A – (f(x))^2, which is clearly maximized when f(x) = 0).
Thus we need to solve the maximization problem (23).
Therefore, we can solve the maximization problem (3) with dual decomposition.
A common approach to solving the maximization problem in (10) in the presence of hidden data is the EM algorithm [33], which is adopted in this work.
Previously, we solve the maximization problem non-causally, which means it is necessary to know the realization of the harvesting energy and the channel in advance in order to determine the optimal transmission power.
At equilibrium, where a t = k t after solving the maximization problem, the capital accumulation function becomes: {overset{k}}_t={k}_t^{alpha }{x}_t^{1-alpha }-{c}_t-updelta {k}_t-{x}_t (7).
The calculation of packet success rate may be the most computationally intensive, but focusing only on the cost of solving the maximization problem, the computational complexity of Algorithm 1 becomes (O(N_{mathrm node}^{2} N_{mathrm packet})) (see the Appendix 1).
Consequently, by using the optimal precoding matrices in the previous hops, the precoding matrix P i−1, i=2,…,N in the current i-th hop can be optimally obtained by solving the maximization problems: max_{bar{mathbf{Q}}geq 0, {sf tr}(bar{mathbf{Q}})leq bar{P}}logdet(mathbf{I}+bar{mathbf{Q}}bar{mathbf{P}}), (29).
Layer 1: solve the maximization Lagrange problem with respect to (p_{{k,n}}^{{m,v}}) under a fix set of Lagrange multipliers.
