论文标题
非平滑DC优化的新信封功能
A new envelope function for nonsmooth DC optimization
论文作者
论文摘要
征收差异（DC）优化问题表明与Lipschitz不同的“包膜”的最小化相当。该替代功能上的梯度方法产生了一种新颖的（子）无梯度近端算法，该算法本质上是可行的，并且可以处理完全非平滑的配方。牛顿型方法（例如L-BFGS）直接适用于经典线路搜索。我们的分析揭示了新颖的DC包膜与前向信封之间的亲属关系，前者是后者的平滑且具有凸度的非线性再培训。
Difference-of-convex (DC) optimization problems are shown to be equivalent to the minimization of a Lipschitz-differentiable "envelope". A gradient method on this surrogate function yields a novel (sub)gradient-free proximal algorithm which is inherently parallelizable and can handle fully nonsmooth formulations. Newton-type methods such as L-BFGS are directly applicable with a classical linesearch. Our analysis reveals a deep kinship between the novel DC envelope and the forward-backward envelope, the former being a smooth and convexity-preserving nonlinear reparametrization of the latter.
