In this article, we present novel multibeam training strategies for millimeter-wave communication systems with the subconnected hybrid architecture. To begin with, we propose an iterative selecting search (ISS) algorithm that can reduce the training complexity of multibeam training by a large margin, and its central concept is exploiting the prior information of scanned beam combinations to iteratively optimize the beam of each subarray in order to determine the possible optimal beam combination. Then, we apply the concept of the ISS algorithm to optimize the original beam set in line with channel sparsity, with the goal of effectively characterizing the large original beam set with a small beam subset, resulting in a much smaller search space for the optimized beam subset than for the original beam set. Furthermore, we adopt two linear search algorithms on our optimized beam subset to develop efficient multibeam training methods. As shown in the simulation results, the ISS scheme shines in terms of low training complexity but performs poorly in spectral efficiency. In comparison to individual linear search methods, beam-subset-optimization-based linear search schemes not only have a greater spectral efficiency, but also have a very low training complexity.