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A proximal gradient method for multiobjective optimization problems with nonmonotone line search
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DOI：10.1080/02331934.2025.2587727.png)
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Abstract
En 中文
This paper proposes a novel nonmonotone proximal gradient method for solving nondifferentiable composite multiobjective optimization problems. The method integrates a nonmonotone line search technique into the proximal gradient framework, offering enhanced flexibility and efficiency for handling nonsmooth or nonconvex objective functions. We analyze the convergence properties of the proposed algorithm, demonstrate that all accumulation points of the generated sequence satisfy Pareto stationarity when the problem is nonconvex. Furthermore, under convexity and mild conditions, we establish that the sequence converges to a weakly Pareto optimal solution of the problem. Numerical experiments on robust multiobjective optimization problems and Lasso multiobjective optimization problems are provided to illustrate the computational efficiency and the practical utility of the proposed method.
Keywords:
Multiobjective optimization
proximal gradient method
Pareto optimality
nonmonotone line search
composite optimization
Journal
O
IF:
1.8
Papers:
121
Citations:
0