刘舒天^*

（  北京邮电大学，信息工程学院；  ）

摘要： 无约束优化问题与常微分方程组的求解有着紧密的联系。本文分析了一种基于信赖域理论的伪轨线追踪算法，这类算法也可以被视为是具有自适应步长调节能力的线性化隐式欧拉法。我们分析了该算法的全局收敛性。进一步，我们将算法应用于求解非线性无约束优化问题。数值算例显示，伪轨线追踪算法相较于传统的常微分方程算法，在稳态点求解方面有着明显的优势。
关键词： 非约束优化；常微分方程组；信赖域；全局收敛性

Shutian Liu^*

（  School of Information Engineering, Beijing University of Posts and Telecommunications；  ）

Abstract： Unconstrained optimization problems are closed related to ordinary differential equations with gradient structure. In this paper, one trust region type method called pseudo-trajectory algorithm is developed. This kind of algorithm can be regarded as linearly implicit Euler method mixed with adaptive trust region time step control. We provide the global convergence analysis. Furthermore, we apply this algorithm to solve nonlinear unconstrained optimization problem. Numerical experiments indicate that the new method is applicable in the problem of finding equilibrium steady state.

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