Hadamard流形上的多目标邻近梯度算法
Proximal Gradient Algorithm forMultiobjective Optimization onHadamard Manifold
DOI: 10.12677/PM.2023.1312367, PDF,    国家自然科学基金支持
作者: 刘仁金, 王湘美*：贵州大学数学与统计学院，贵州 贵阳
关键词: Hadamard流形；邻近梯度算法；Polyak-Loiasiewicz不等式；Hadamard Manifold； Proximal Gradient Algorithm； Polyak-Lojasiewicz Inequality
摘要: 邻近梯度算法是求解非光滑优化问题的经典算法。本文将多目标优化问题的邻近梯度算法推广到Hadammard流形上。在一定条件下，证明了算法产生序列的聚点是Pareto稳定点。在目标函数满足Polyak-Loiasiewicz不等式时，得到算法的收敛速度是线性的。所得结果在Hadamard流形上是新的。
Abstract: Proximal gradient algorithm is a classical algorithm for solving nonsmooth optimiza- tion problems. In this paper, the multiobjective proximal gradient algorithm is ex- tended to Hadamard manifold. Under certain conditions, it is proved that the cluster point of the sequence generated by the algorithm is Pareto stationary. In the case, when the objective function satisfies the Polyak-Lojasiewicz inequality, the conver- gence rate of the algorithm is linear.
文章引用：刘仁金, 王湘美. Hadamard流形上的多目标邻近梯度算法[J]. 理论数学, 2023, 13(12): 3525-3536. https://doi.org/10.12677/PM.2023.1312367

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