标题： 在 l1-球上使用活动集非单调投影梯度进行最小化 显示英文标题

标题： Minimization over the l1-ball using an active-set non-monotone projected gradient

摘要： l1-ball是一个结构良好的可行集，广泛用于许多领域（例如，机器学习、统计和信号分析）以在模型解中强制某些稀疏性。 在本文中，我们设计了一种有效处理l1-ball上最小化问题的活动集策略，并将其嵌入到一种定制的算法框架中，该框架利用非单调的一阶方法在每次迭代中探索给定的子空间。 我们证明了全局收敛到驻点。 最后，我们在两类不同的实例上报告了数值实验，展示了该算法的有效性。 显示英文摘要

摘要： The l1-ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the l1-ball and embed it into a tailored algorithmic scheme that makes use of a non-monotone first-order approach to explore the given subspace at each iteration. We prove global convergence to stationary points. Finally, we report numerical experiments, on two different classes of instances, showing the effectiveness of the algorithm.