We consider a projected gradient method equipped with the nonmonotone line search procedure for convex constrained multiobjective optimization problems. Under mild assumptions, we show the convergence of the full sequence generated by the algorithm to a weak Pareto optimal point. Furthermore, under some appropriate Lipschitz continuity assumption of the gradients of objective functions, a linear convergence result for this method is also established.

中文翻译：

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用于多目标优化的非单调投影梯度方法的线性收敛

我们考虑了一种投影梯度方法，该方法配备了用于凸约束多目标优化问题的非单调线搜索程序。在温和的假设下，我们展示了算法生成的全序列收敛到弱帕累托最优点。此外，在目标函数梯度的一些合适的Lipschitz连续性假设下，也建立了该方法的线性收敛结果。