论文标题
快速投射到有序加权$ \ ell_1 $ norm ball上
Fast projection onto the ordered weighted $\ell_1$ norm ball
论文作者
论文摘要
在本文中，我们提供了一种有限终止但有效的方法，将欧几里得投射计算到有序的加权$ \ ell_1 $（OWL1）Norm Ball上。特别是，提出了一种有效的半齿牛顿方法来解决原始投影问题的重新印度的双重化。证明了算法的全球和局部二次收敛结果以及有限终止属性。与两种最著名方法的数值比较证明了我们方法的效率。此外，我们得出了研究投影仪的广义雅各布式，我们认为这对于未来设计快速二阶非平滑方法的方法至关重要，以解决一般的OWL1规范约束问题。
In this paper, we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted $\ell_1$ (OWL1) norm ball. In particular, an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem. Global and local quadratic convergence results, as well as the finite termination property, of the algorithm are proved. Numerical comparisons with the two best-known methods demonstrate the efficiency of our method. In addition, we derive the generalized Jacobian of the studied projector which, we believe, is crucial for the future designing of fast second order nonsmooth methods for solving general OWL1 norm constrained problems.
