基于线性模型的自适应信赖域方法

An Adaptive Trust Region Method Based on Linear Models

为求解大规模无约束优化问题,本文提出了一种自适应线性信赖域法。与传统的线性信赖域法相比,新方法借助一数量矩阵近似Hesse阵,并据此计算线性信赖域半径。理论上证明了新算法的全局收敛性,数值实验表明新算法非常适合大规模问题的求解。

An adaptive linear trust region method is designed to solve large scale unconstrained optimization problems. Unlike the traditional linear trust region method, the new algorithm gets the trust region radius of the linear model by using a new scalar approximation of the minimizing function~ Hessian. The convergence results of the method are proved under certain conditions. Numerical results show that the new method is very effective and attractive for large scale unconstrained problems.