A Nonmonotone Projected Gradient Method for Multiobjective Problems on Convex Sets

被引：0
作者：
Gabrie Aníbal Carrizo
Nadia Soledad Fazzio
María Laura Schuverdt
机构：
[1] National University of the South,Department of Mathematics
[2] University of La Plata,Department of Mathematics
来源：
Journal of the Operations Research Society of China | 2024年 / 12卷
关键词：
Multiobjective optimization; Projected gradient methods; Nonmonotone line search; Global convergence; 90C29; 49M37; 65K05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this work we consider an extension of the classical scalar-valued projected gradient method for multiobjective problems on convex sets. As in Fazzio et al. (Optim Lett 13:1365–1379, 2019) a parameter which controls the step length is considered and an updating rule based on the spectral gradient method from the scalar case is proposed. In the present paper, we consider an extension of the traditional nonmonotone approach of Grippo et al. (SIAM J Numer Anal 23:707–716, 1986) based on the maximum of some previous function values as suggested in Mita et al. (J Glob Optim 75:539–559, 2019) for unconstrained multiobjective optimization problems. We prove the accumulation points of sequences generated by the proposed algorithm, if they exist, are stationary points of the original problem. Numerical experiments are reported.
引用
收藏
页码：410 / 427
页数：17
相关论文
共 43 条
[1]  
Fukuda EH(2011)On the convergence of the projected gradient method for vector optimization Optimization 60 1009-1021
[2]  
Graña Drummond LM(2013)Inexact projected gradient method for vector optimization Comput. Optim. Appl. 54 473-493
[3]  
Fukuda EH(2014)A survey on multiobjective descent methods Pesq. Oper. 34 585-620
[4]  
Graña Drummond LM(2004)A projected gradient method for vector optimization problems Comput. Optim. Appl. 28 5-29
[5]  
Fukuda EH(2019)Convergence analysis of a nonmonotone projected gradient method for multiobjective optimization problems Optim. Lett. 13 1365-1379
[6]  
Graña Drummond LM(1986)A nonmonotone line search technique for Newton’s method SIAM J. Numer. Anal. 23 707-716
[7]  
Graña Drummond LM(2019)Nonmonotone line searches for unconstrained multiobjective optimization problems J. Glob. Optim. 75 63-90
[8]  
Iusem AN(2017)Nonmonotone gradient methods for vector optimization with a portfolio optimization application Eur. J. Oper. Res. 263 356-366
[9]  
Fazzio NS(2004)A nonmonotone line search technique and its application to unconstrained optimization SIAM J. Opt. 14 1043-1056
[10]  
Schuverdt ML(1999)Nonmonotone spectral projected gradient methods on convex sets SIAM J. Optim. 10 1196-1211
12345