Guo Yanni, Cui Wei
College of Science, Civil Aviation University of China, Tianjin, China.
J Inequal Appl. 2018;2018(1):103. doi: 10.1186/s13660-018-1695-x. Epub 2018 May 2.
The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this paper, we introduce a modified proximal gradient algorithm with outer perturbations in Hilbert space and prove that the algorithm converges strongly to a solution of the composite optimization problem. We also discuss the bounded perturbation resilience of the basic algorithm of this iterative scheme and illustrate it with an application.
近端梯度算法是求解非光滑复合优化问题的一种有吸引力的方法，在无限维情形下它可能只有弱收敛性。在本文中，我们在希尔伯特空间中引入一种带外部扰动的修正近端梯度算法，并证明该算法强收敛到复合优化问题的一个解。我们还讨论了这种迭代格式基本算法的有界扰动弹性，并通过一个应用加以说明。
