论文标题
有效的正则近端准牛顿方法，用于大规模非凸复合综合优化问题
Efficient Regularized Proximal Quasi-Newton Methods for Large-Scale Nonconvex Composite Optimization Problems
论文作者
论文摘要
复合功能的优化问题由一个目标函数组成，该目标函数是平滑和（凸）非平滑项的总和。这种特殊的结构是由近端方法类别及其某些概括（例如牛顿近端和准Newton方法）所利用的。在本文中，我们提出了一种正规化的准牛顿方法，其主要特征是：（a）该方法在全球范围内收敛到固定点，（b）全球化由正规化参数控制，不需要线搜索，（c）该方法可以基于一个非常有效的观察来实现，该观察是为了结合了Quasimi-Newton troxim-newton troxim-newton troxtor and Quasimi-newton troxsimentity comptory的最新想法，准Newton的更新。解决方案和非Convex复合优化问题的数值示例表明该方法的表现优于几种现有方法。
Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. In this paper, we propose a regularized proximal quasi-Newton method whose main features are: (a) the method is globally convergent to stationary points, (b) the globalization is controlled by a regularization parameter, no line search is required, (c) the method can be implemented very efficiently based on a simple observation which combines recent ideas for the computation of quasi-Newton proximity operators and compact representations of limited-memory quasi-Newton updates. Numerical examples for the solution of convex and nonconvex composite optimization problems indicate that the method outperforms several existing methods.
