We formulate the resource allocation in the downlink of heterogeneous orthogonal frequency division multiple access (OFDMA) networks. Our main objective is to maximize the system sum throughput subject to service and system constraints, including maximum transmit power, quality of service and peruser subchannel allocation. Due to the inter-cell interference the corresponding optimization problem is, in fact, nonconvex, that cannot be solved using standard convex optimization techniques. Here we propose an algorithm based on local search method and use of penalty function to approximate the formulated constrained optimization problem by an unconstrained one. To approximate a global optimal, we set escaping procedure from critical point based on constraint function conditions. The result shows that the proposed method might achieve optimum conditions by a hybrid of split and shared spectrum allocation. Numerical analysis indicates that the proposed algorithm outperform the other conventional methods in the scenario of high level of inter-cell interference with high number of users. In the case of small number of users, we further observe that the proposed method performs better than equal power allocation method (EPA). Moreover, the proposed method approximates the global optimum by considering channel gain and inter-cell interference with a fast rate of convergence.