In this paper, we construct a novel algorithm for solving non-smooth composite optimization problems. By using inertial technique, we propose a modified proximal gradient algorithm with outer perturbations, and under standard mild conditions, we obtain strong convergence results for finding a solution of composite optimization problem. Based on bounded perturbation resilience, we present our proposed algorithm with the superiorization method and apply it to image recovery problem. Finally, we provide the numerical experiments to show efficiency of the proposed algorithm and comparison with previously known algorithms in signal recovery.

中文翻译：

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应用于信号恢复的惯性近端梯度算法的优越化方法和扰动弹性

在本文中，我们构建了一种解决非光滑复合优化问题的新算法。通过使用惯性技术，我们提出了一种改进的具有外扰动的近端梯度算法，并且在标准温和条件下，我们获得了寻找复合优化问题解的强收敛结果。基于有界扰动弹性，我们提出了我们提出的算法和优胜方法，并将其应用于图像恢复问题。最后，我们提供了数值实验来展示所提出算法的效率，并与先前已知的信号恢复算法进行比较。