Tian Ming, Zhang Hui-Fang
College of Science, Civil Aviation University of China, Tianjin, 300300 China ; Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin, 300300 China.
College of Science, Civil Aviation University of China, Tianjin, 300300 China.
J Inequal Appl. 2017;2017(1):13. doi: 10.1186/s13660-016-1289-4. Epub 2017 Jan 9.
Let be a real Hilbert space and be a nonempty closed convex subset of . Assume that is a real-valued convex function and the gradient ∇ is [Formula: see text]-ism with [Formula: see text]. Let [Formula: see text], [Formula: see text]. We prove that the sequence [Formula: see text] generated by the iterative algorithm [Formula: see text], [Formula: see text] converges strongly to [Formula: see text], where [Formula: see text] is the minimum-norm solution of the constrained convex minimization problem, which also solves the variational inequality [Formula: see text], [Formula: see text]. Under suitable conditions, we obtain some strong convergence theorems. As an application, we apply our algorithm to solving the split feasibility problem in Hilbert spaces.
设 为实希尔伯特空间， 为 的非空闭凸子集。假设 是实值凸函数且梯度∇是具有 的[公式：见原文]-ism。设 ， 。我们证明由迭代算法 ， 生成的序列 强收敛于 ，其中 是约束凸最小化问题的最小范数解，它也解决变分不等式 ， 。在适当条件下，我们得到一些强收敛定理。作为应用，我们将我们的算法应用于解决希尔伯特空间中的分裂可行性问题。
