Hadamard流形上的多目标邻近梯度算法

Proximal Gradient Algorithm forMultiobjective Optimization onHadamard Manifold

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。

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 clusterpoint 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.