This paper studies the rate maximization problem of a Full duplex(FD) D2D underlaying cellular network. In the considered scenario, multiple FD-D2D pairs coexist with multiple cellular users which generate mutual interference between the two communication types. The complicated interference environment makes the optimization problem a non-concave problem. To solve this problem, we discuss how to leverage the monotonic optimization theory to obtain the global optimal solution at the cost of high complexity. We also derive a geometric based optimization framework, denoted as GALEN, that achieves the global optimality with much lower complexity, and also it provides a closed form expression for the solution. The simulation results show the importance of the proposed solution. Index Terms-full-duplex transmission, device-to-device (D2D) communication, optimal power allocation, duplex mode selection