无约束优化中的张量方法

对于非线性方程组解的Jacobian矩阵是奇异的情况,将非线性函数在当前迭代点的线性模型扩展成二次模型,然后将目标函数是二次张量模型的范数优化问题转化成四次张量优化问题,以便用适当的张量方法求解。

A Tensor Method in Unconstrained Optimization

For system of nonliner equations where the Jacobian matrix at the solution is singular, we expand the linear model at the current point to the quadratic model,then convert the optimization problem whose objective function is a norm of second-order tensor model into a fourth-order tensor model so that we can solve it with the proper tensor method.