向量优化广义牛顿法的Kantorovich型定理

Kantorovich Type Theorem of Extended Newton Method for Vector Optimization

研究求解无约束向量优化问题的广义牛顿法的半局部收敛性,建立了广义牛顿法的Kantorovich型收敛定理.在初始点附近,目标函数满足强K-凸性质,其二阶导数满足Lipschitz性质.相关参数满足某些假设的情况下,得到了该算法二阶收敛性且收敛到向量优化问题的解,同时给出了误差估计.

This paper considered the semi local convergence property of the extended Newton method for unconstrained vector optimization problems,and established the Kantorovich type convergence theorem of the extended Newton method.More precisely,when the objective function was strongly K-convex near the initial point,its second derivative satisfied the Lipschitz condition,and some parameters related to the initial point satisfy certain conditions.It was obtained that the sequence generated by the algorithm quadratically converged to a K-minimizer of the vector optimization problem.At the same time,the error estimate was provided.