CONVERGENCE RATE OF GRADIENT DESCENT METHOD FOR MULTI-OBJECTIVE OPTIMIZATION  

作　　者：Liaoyuan Zeng Yuhong Dai Yakui Huang 

机构地区：[1]Institute of Computational Mathematics and Scientific/Engineering Computing,State Key Labomtory of Scientific and Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Science,Hebei University of Technology,Tianjin 300401 ,China

出　　处：《Journal of Computational Mathematics》2019年第5期689-703,共15页计算数学（英文）

基　　金：The authors are grateful for the valuable comments and suggestions of two anonymous referees;The authors also would like to thank Dr. Hui Zhang in National University of Defense Technology for his many suggestions and comments on an early draft of this paper;This research is supported by the Chinese Natural Science Foundation (Nos. 11631013, 11971372);the National 973 Program of China (Nos. 2015CB856002).

摘　　要：The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP). Under standard assumptions, we prove that the gradient descent method with constant stepsizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if the objective functions are strongly convex. The results are also extended to the gradient descent method with the Armijo line search. Hence, we see that the gradient descent method for MOP enjoys the same convergence properties as those for scalar optimization.

关 键 词：MULTI-OBJECTIVE optimization GRADIENT DESCENT CONVERGENCE rate. 

分 类 号：O1[理学—数学]