信赖域子问题求解方法及其数值试验研究

Study on the Solution Methods and Numerical Tests of Trust Region Subproblem

信赖域算法是目前求解无约束优化问题的一种重要的数值计算方法,而信赖域子问题的求解则是实现信赖域算法的关键。阐述求解信赖域子问题的3种方法(不定折线法、Moré-Sorensen法以及截断共轭梯度法),利用国际上广泛采用的无约束优化测试函数包对以上3种方法进行大量的数值试验。结果表明截断共轭梯度法的数值计算效率在一定程度上优于其他两种方法,非单调的信赖域算法在一定程度上优于传统的单调算法。

Trust region algorithm is an important numerical method to solve unconstrained optimization problems at present,and the solution of trust region subproblem is the key to realizing the trust region algorithm. In this paper,three methods for solving trust region subproblems(indeterminate broken line method,Moré-Sorensen method and truncated conjugate gradient method) are described. A large number of numerical tests are carried out on the above three methods by using the unconstrained optimization test function package widely used in the world. The results show that to some extent,the efficiency of the truncated conjugate gradient method is better than the other two methods,and the non-monotone trust region algorithm is better than the traditional monotone algorithm to some extent.