求解多目标优化问题的非单调牛顿法的超线性收敛性  

Superlinear Convergence of Nonmonotone Newton Method for Solving Multiobjective Optimization Problems

作　　者：任洁 彭建文 REN Jie;PENG Jianwen(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《应用数学》2022年第4期956-965,共10页Mathematica Applicata

基　　金：国家自然科学基金重大项目(11991024);重庆英才·创新创业领军人才·创新创业示范团队项目(CQYC20210309536);重庆市高校创新研究群体项目(CXQT20014)。

摘　　要：讨论求解无约束多目标优化问题的非单调牛顿法的全局收敛性和局部超线性收敛率.首先,给出由非单调牛顿法生成的步长的下界,再利用求解多目标优化问题的牛顿法的相关结论证明了非单调牛顿法的全局收敛性.其次,在目标函数的海塞矩阵的一致连续性的条件下证明了非单调牛顿法具有局部超线性收敛率.The global convergence and local superlinear convergence rate of the nonmonotone Newton method for solving unconstrained multiobjective optimization problems was discussed.Firstly,the lower bound of the step size generated by the nonmonotone Newton method was given,and the global convergence of the nonmonotone Newton method was proved by the relevant conclusions of the Newton method for solving multiobjective optimization problems.Secondly,under the condition of uniform continuity of the Hessian matrix of the objective function,it was proved that the nonmonotone Newton method has local superlinear convergence rate.

关 键 词：多目标优化 非单调线搜索 非单调牛顿法 Pareto平稳性 超线性收敛率 

分 类 号：O221.6[理学—运筹学与控制论]