论文标题
非凸复合稀疏优化问题的丰富二阶方法
An enriched second-order method for nonconvex composite sparse optimization problems
论文作者
论文摘要
在本文中，我们提出了一种用于求解\ emph {线性复合稀疏优化问题}的第二级方法，该方法包括最小化可区分（可能是非convex函数）和非不同的凸项的总和。 $ \ ell_1 $ - 矩阵的标准与系数向量乘以$ \ ell_1 $给出了复合非不同的凸点。我们针对线性复合$ \ ell_1 $问题提出的算法取决于为Oesom算法\ cite {dlrlm07}启动的三种主要成分：最小规范次级次级，投影步骤，尤其是与Nondiffiffiftiffifferrent ferfifferentifferrent term forsement of term offiencations步骤。通过扩展这些设备，我们获得了解决复合稀疏优化问题的完整第二阶方法，其中包括广泛的应用程序。例如，涉及一般类\ emph {dindinial图操作员}的最小化问题可以使用所提出的算法解决。我们提出了几项计算实验，以显示我们方法在不同应用示例中的效率。
In this paper we propose a second--order method for solving \emph{linear composite sparse optimization problems} consisting of minimizing the sum of a differentiable (possibly nonconvex function) and a nondifferentiable convex term. The composite nondifferentiable convex penalizer is given by $\ell_1$--norm of a matrix multiplied with the coefficient vector. The algorithm that we propose for the case of the linear composite $\ell_1$ problem relies on the three main ingredients that power the OESOM algorithm \cite{dlrlm07}: the minimum norm subgradient, a projection step and, in particular, the second--order information associated to the nondifferentiable term. By extending these devices, we obtain a full second--order method for solving composite sparse optimization problems which includes a wide range of applications. For instance, problems involving the minimization of a general class \emph{differential graph operators} can be solved with the proposed algorithm. We present several computational experiments to show the efficiency of our approach for different application examples.
