论文标题
通过近端分裂算子的杂化最陡下降法优化层次凸的凸凸 - SVM和Lasso的增强
Hierarchical Convex Optimization by the Hybrid Steepest Descent Method with Proximal Splitting Operators -- Enhancements of SVM and Lasso
论文作者
论文摘要
现代近端分裂方法中的突破性想法使我们能够表达出多个非平滑凸的叠加叠加的所有最小化器的集合，作为可计算的非二手操作员的固定点集。在本文中，我们提出了用于层次凸优化问题的实用算法策略，这些策略需要从标准凸优化的解决方案集中进一步战略性地选择最可取的向量。提出的算法是通过将杂化最陡峭的下降方法应用于通过近端分裂艺术设计的特殊非专业算子来确定的。我们还向拟议的策略提出了对支持向量机和套索估计器的某些未开发的层次增强的应用。
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In this paper, we present practical algorithmic strategies for the hierarchical convex optimization problems which require further strategic selection of a most desirable vector from the solution set of the standard convex optimization. The proposed algorithms are established by applying the hybrid steepest descent method to special nonexpansive operators designed through the art of proximal splitting. We also present applications of the proposed strategies to certain unexplored hierarchical enhancements of the support vector machine and the Lasso estimator.
