求解约束多目标优化问题的一种Barzilai-Borwein投影梯度法研究  

A Study on Barzilai Borwein Projection Gradient Algorithmfor Solving Constrained Multi-objective Optimization Problems

作　　者：张丹[1] 刘宝钰 ZHANG Dan;LIU Bao-yu(National Center for Applied Mathematics in Chongqing,Chongqing Normal University,Shapingba401331,Chongqing)

机构地区：[1]重庆师范大学重庆国家应用数学中心,重庆沙坪坝401331

出　　处：《商洛学院学报》2024年第6期16-22,共7页Journal of Shangluo University

基　　金：重庆师范大学研究生科研创新项目(YKC23037)。

摘　　要：基于Barzilai-Borwein规则使用不同的平衡因子来调节目标函数之间的平衡性,减少多目标投影梯度算法受目标函数之间不平衡的影响,提出了一种Barzilai-Borwein投影梯度法(BBPMG法)。在一定的假设条件下,BBPGM法具有良好的收敛性。同时对BBPGM法进行大量的数值试验,结果表明BBPGM法具有更好的数值性能。Based on Barzilai-Borwein rule,this study proposes a Barzilai-Borwein projection gradient method(BBPGM)that uses different balancing factors to adjust the balance among objective functions,thereby reducing the impact of imbalance between objective functions on the multiobjective projection gradient algorithm.Under certain assumptions,the BBPGM method exhibits good convergence properties.A large number of numerical experiments are also conducted on the BBPGM method,and the results show that the BBPGM method has better numerical performance.

关 键 词：约束多目标优化问题 投影梯度算法 Barzilai-Borwein规则 收敛性 

分 类 号：O221[理学—运筹学与控制论]