Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity
研究了在目标函数光滑部分仅满足局部Lipschitz梯度连续性的非凸复合优化问题，提出一种自适应PANOC型加速线搜索算法，仅需近端梯度的简单预言机，并允许近端映射的不精确计算，扩展了现有优化软件的性能。
Abstract Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local Lipschitz gradient continuity for the smooth part of the objective function. We investigate an adaptive scheme for PANOC-type methods (Stella et al. in Proceedings of the IEEE 56th CDC, 2017), namely accelerated linesearch algorithms requiring only the simple oracle of proximal gradient. While including the classical proximal gradient method, our theoretical results cover a broader class of algorithms and provide convergence guarantees for accelerated methods with possibly inexact computation of the proximal mapping. These findings have also significant practical impact, as they widen scope and performance of existing, and possibly future, general purpose optimization software that invoke PANOC as inner solver.