Power allocation. Power allocation problem is a fundamental optimization problem in communica$-$ tions systems. This problem arises in scenarios where a transmitter aims to allocate its available power across several concurrent communication channels to maximize the total data rate. We are given N communication channels, i$=1,2,$dots,N$.$ Each channel has a different noise level n$\_($i$)($given$),$ and is allocated power p$\_($i$)$ to transmit at$.$ It can achieve a transmission rate R$\_($i$)=$log$\_(2)(1+($p$\_($i$))/($n$\_($i$))).$ The goal of the problem is to find the optimal power allocation p$\_($i$)$ that each channel should transmit at$.$ The mathematical formulation of the problem can be described as maximizing the sum of the transmission rates R$\_($i$)($called the "sum rate"$),$ while ensuring