求解带有稀疏约束和闭凸集约束的优化问题的投影算法
A Projection Algorithm for Solving Optimization Problems with Sparsity Constraints and Closed Convex Set Constraints
DOI: 10.12677/ORF.2017.73009, PDF, HTML, XML, 下载: 1,510  浏览: 3,504  国家自然科学基金支持
作者: 孙 军*, 屈 彪：曲阜师范大学管理学院，山东 日照
关键词: 稀疏约束；闭凸集约束；收敛；α-稳定点；Sparsity-Constrained； Closed Convex Set Constraints； Convergence；α-Stationary Point
摘要: 本文中，我们考虑了带有稀疏约束和闭凸集约束的优化问题的求解。设计了一种带有Armijo步长规则的梯度投影算法，证明了此算法产生的迭代点列可以收敛到问题的一个α-稳定点上。最后给出了数值例子验证了算法的有效性。
Abstract: In this paper, we mainly consider the optimization problem with sparsity constraints and closed convex set constraints. We design a gradient projection algorithm with Armijo step size rule, and prove that the sequence of the iteration generated by this algorithm can converge to an α-stationary point of the problem. Finally, a numerical example is given to demonstrate the effec-tiveness of the algorithm.
文章引用：孙军, 屈彪. 求解带有稀疏约束和闭凸集约束的优化问题的投影算法[J]. 运筹与模糊学, 2017, 7(3): 73-80. https://doi.org/10.12677/ORF.2017.73009

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