We consider the resource allocation (RA) optimization problem in shared spectrum access communications system, and propose efficient solutions for both inter-operator and intra-operator RA optimization problems. For inter-operator RA optimization, we present a spectrum sharing framework that primarily focuses on fairness issues for the spectrum sharing operators, by taking care of the sharing policy measures. For intra-operator RA, a joint subcarrier and power allocation scheme is considered for throughput maximization of a spectrum sharing operator employing exclusive assignment of subcarriers to its users under transmitting power constraint. Since the optimization problem is combinatorial with nonlinear constraints and has non-convex feasible regions, it is numerically very difficult to solve. We propose an efficient solution by linearizing and/or linearly approximating the nonlinear constraints, and by applying a transformation to a second order cone program form to handle the nonlinear objective function. The simulation results demonstrate the efficiency of the proposed solutions.