Improved Algorithm for Solving Trust Region Sub-problem Based on Adams Two-Step Algorithm

Abstract

In large-scale trust region subproblem solving, direct Adams two-step algorithm for large-scale trust region solution will result in huge memory requirement and long computing time. To solve this problem, an adaptive Adams two-step algorithm is proposed to solve the trust region subproblem. This method utilizes the characteristic of Adams two-step algorithm to reduce the dimension and reduces the matrix size through adaptive Adams two-step algorithm until it can be solved directly by Adams two-step algorithm. In the process of adaptive Adams two-step algorithm, the matrix is decomposed into many submatrices that are small enough, and the trust region subproblem solving is transformed into the two-step iterative computation of Adams, and the large-scale problem is transformed into a series of small-scale operations. At the same time, the concurrency can be found, and the trust region subproblem can be solved and the running speed can be improved. The experimental results show that even serial processing can greatly reduce the time and space cost of solving the large-scale trust region subproblem, and the speedup ratio of solving the trust region subproblem is close to 300 under the condition of two computers. The convergence of the whole solution process is good.