Device-to-Device (D2D) communications underlaying cellular networks have emerged as a necessity for a substantial increase in the system throughput and the number of active devices for the future cellular networks. In underlay D2D networks, it is conventional to use different interference management (IM) techniques to allow D2D transmitters to reuse the cellular users' subcarriers. Conventionally, those IM techniques pair a specific number (one or more) of D2D transmitters to each subcarrier and/or allow each D2D transmitter to transmit on a specific number of subcarriers simultaneously in order to achieve the target rates. Due to the mixed-integer nature of those IM techniques, convex optimization techniques can not be used, and usually complex heuristic or game-theoretic approaches are exploited. In this paper, we introduce a reduced-constraints approach to seek sub-optimal joint power allocation and channel assignment solutions for two non-convex, mixed-integer, and non-linear programs (MINLP). Specifically, via the reduced-constraints approach and variable transformation techniques, we can exploit primal-dual algorithms to solve system power minimization and energy-efficiency maximization problems. Extensive numerical simulation results show that the proposed approach outperforms state-of-the-art techniques.