无约束优化问题的牛顿谱梯度法

Newton Spectral Gradient Method of Unconstrained Optimization Problems

摘要: 本文在Newton法和最速下降法的组合方法的基础上提出求解无约束优化问题的Newton法与谱梯度法的组合方法，该方法有效地应用于目标函数的Hessian矩阵不正定或初始点不接近极小点的问题，并利用非单调线搜索求解步长。在较温和的条件下建立了该方法的全局收敛性和超线性收敛性，并且数值实验证明了该算法具有很好的数值实验效果。

Abstract: Based on the Newton method and the combination of the steepest descent method, Newton method and spectral gradient method are combined to solve unconstrained optimization prob-lems. This method is effectively applied to the problem that the Hessian matrix of the objective function is not positive definite or the initial point is not close to the minimum point, and the non-monotone line search is used to solve the step size. The global convergence and superlinear convergence of this method are established under relatively mild conditions, and the numerical experiments show that the algorithm has good numerical experimental results.