In the achievable rate region maximization for intelligent reflecting surfaces (IRSs)-assisted interference channel (IFC), where more than one pair of transceivers communicates and interferes with each other simultaneously. Specifically, we optimize the transmit power and passive beamforming vectors at all the IRSs to obtain the Pareto boundary of the achievable rate region in IFC, subject to the unit-modulus constraints for the passive beamforming vectors at the IRSs and transmit power budgets at the transmitters. To solve the formulated non-convex optimization problem efficiently, we resort to optimize each variable alternatively until convergence. The optimization of transmit power is based on a locally optimal fixed-point iteration method. Instead of using the conventional high-complexity and sub-optimal Gaussian randomization-aided semi-definite relaxation (SDR) technique for the passive beamforming design, we first propose a novel locally optimal homotopy optimization based majorization-minimization method. To further reduce the computational complexity, a locally optimal log-sum-exp approximation based manifold optimization method is also proposed. Simulation results validate that our proposed methods can significantly decrease the computational complexity and outperform the conventional SDR-based algorithm.