The traditional satellite transparent relay mode causes significant delays in the new satellite-ground network. In order to improve the service capability for ground users, this paper proposes a caching scheme on both the Low-Earth Orbit(LEO) satellite and the ground content server,and models the transmission throughput problem of the satellite-ground network considering cofrequency interference among LEO satellites, ground content servers, and ground users. The improved Particle Swarm Optimization(PSO) algorithm and the Supporting Hyperplane Optimization Toolkit(SHOT) solver are employed to solve the problem. The experimental results reveal that the SHOT solver can obtain a smoother result curve, and there is only about 2% fluctuation compared to the optimization PSO algorithm and the SHOT solver. Under the constraint of an 8 dB signal-to-noise ratio threshold and a maximum power of 20 W, the proposed approach can achieve a transmission rate of 45 Mbps and 37 Mbps, respectively, with interference from 2 satellites or 3 ground content servers. Furthermore, the study analyzes the running time of the two algorithms for various numbers of low-earth orbit satellites,ground content servers, and ground users. The optimization PSO algorithm is approximately 10 s faster than the SHOT solver, particularly when the number of the three categories is set to 4, in the worst-case scenario. The results indicate that heuristic algorithms are more suitable for modeling future complex satellite-ground networks and finding non-convex and nonlinear global solutions. They also perform better in terms of solving speed for high-dimensional problems.