We address the throughput maximization problem for downlink transmission in decode-and-forward (DF) relay-assisted cognitive radio networks (CRNs) based on simultaneous wireless information and power transfer (SWIPT) capability. In this assumed network, the multiple-input multiple-output (MIMO) relay and secondary user (SU) equipment are designed to operate with the energy harvest from radio frequency (RF) signals as well as SWIPT capability. Also, the cognitive base station (CBS) communicates with SU just through a MIMO relay. Based on the considered network model, multiple combinatorial constraints in the main problem complicate the solution. So, this paper applies heuristic policies in the convex optimization framework to tackle this complexity. First, the throughput maximization problem is considered for the two sides of the relay separately. Second, we progress towards solving each side's complicated problem optimally by recruiting subproblems solving strategy. Finally, these optimum solutions are integrated by proposing a heuristic iterative power assignment algorithm in which combinatorial constraints are satisfied with low convergence time. The proposed algorithm performance is evaluated in comparison with benchmark algorithms via numerical outcomes in respect of optimality, convergence time, and compliance with constraints.