Full-duplex (FD) communication is promoted to double the spectral efficiency when compared to the halfduplex (HD) counterpart. In the context of cellular networks, however, FD communication exacerbates the aggregate uplink and downlink interference, which diminishes the foreseen FD gains. This paper considers a flexible duplex system, denoted by -duplex (-D) system, wherein a fine-grained bandwidth control for each uplink/downlink channel pair in each base station (BS) is allowed, which also leads to partial spectrum overlap between the uplink and downlink channels. The paper addresses the resulting interference management problem by maximizing a network-wide rate-based utility function subject to uplink/downlink power constraints, so as to determine userto- BS association, user-to-channel scheduling, the UL and DL transmit powers, and the fraction of spectrum overlap between UL and DL for every user, under the assumption that the number of available channels and users are equal. The paper solves such a non-convex mixed-integer optimization problem in an iterative way by decoupling the problem into several subproblems. Particularly, the user-to-BS association problem is solved using a matching algorithm that is a generalization of the stable marriage problem. The scheduling problem is solved by iterative Hungarian algorithm. The power and spectrum overlap problem is solved by successive convex approximation. The proposed iterative strategy guarantees an efficient one-toone user to BS and channel assignment. It further provides optimized flexible duplexing and power allocation schemes for all transceivers. Simulations results show appreciable gains when comparing the proposed solution to different schemes from the literature.