关键词: 信赖域子问题, 微分方程模型, 不定矩阵, Heun三阶算法

Abstract: For the trust region subproblems, it is modified by Bunch-Parlett method when the Hessian matrix is indefinite. In addition, symmetric positive-definite matrix is also constructed, and the stator problem is transformed into a positive-definite subproblem. The Heun third-order algorithm is given by using a new polygonal line to approximate the solution curve. Then, the feasibility of this algorithm is theoretically proved by analyzing the properties of path of Heun third-order polyline. Finally, the numerical experiments of two test-function show that the algorithm is effective.

Key words: trust region subproblems, differential equation model, indefinite matrix, Heun third-order algorithm