向量优化广义牛顿法的Kantorovich型定理  

Kantorovich Type Theorem of Extended Newton Method for Vector Optimization

作　　者：鞠豪 张露方 李尹 JU Hao;ZHANG Lufang;LI Yin(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China;School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121 [2]浙江科技大学理学院,浙江杭州310023

出　　处：《杭州师范大学学报（自然科学版）》2024年第5期555-564,共10页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LQ24A010023);浙江科技大学青年科学基金项目(2023QN055).

摘　　要：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.

关 键 词：向量优化 牛顿法 半局部收敛 优函数 LIPSCHITZ条件 

分 类 号：O224[理学—运筹学与控制论]