A NONMONOTONE GRADIENT METHOD FOR CONSTRAINED MULTIOBJECTIVE OPTIMIZATION PROBLEMS

被引：35

作者：

Zhao, Xiaopeng ^{[1
]}

Yao, Jen-chih ^{[2
]}

Yao, Yonghong ^{[1
]}

机构：

[1] Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China

[2] China Med Univ, China Med Univ Hosp, Res Ctr Interneural Comp, Taichung 40447, Taiwan

来源：

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS | 2022年 / 6卷 / 06期

基金：

中国国家自然科学基金;

关键词：

  Gradient method; Linear convergence; Multiobjective optimization; Nonmonotone line search; Pareto optimality; LINE SEARCH TECHNIQUE; VECTOR OPTIMIZATION; CONVERGENCE; DESCENT; ALGORITHMS;

D O I：

10.23952/jnva.6.2022.6.07

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a nonmonotone gradient method for smooth constrained multiob-jective optimization problems. Under mild assumptions, we demonstrate the Pareto stationarity of the accumulation point of the sequence generated by this method, while the convergence of the full sequence to a weak Pareto optimal solution of the problem is proven when the function is convex. Further, by im-posing some assumptions on the gradients of the objective functions and the search directions, the linear convergence of the function value sequence to the optimal value is provided. The initial point in the convergence results established here can be any one in the constraint set.

引用

页码：693 / 706

页数：14

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