题    目：General inertial proximal gradient method with gradient extrapolation for nonconvex nonsmooth optimization problems

主讲人：蔡邢菊 教授

单    位：南京师范大学

时    间：2024年11月10日 10:00 15:00

地    点：郑州校区九章学堂南楼C座302

摘    要：The inertial strategy has been widely utilized to accelerate proximal gradient methods for nonconvex nonsmooth optimization problems. Recently, the gradient extrapolation technique has also been adopted to further enhance the acceleration of these methods. Inspired by the effectiveness of both techniques, in this paper, we propose a general inertial proximal gradient method with gradient extrapolation, named GiPMGE. Compared to existing methods, our proposed GiPMGE not only covers some classical methods, but also offers more general and flexible choices for the inertial and gradient extrapolation parameters. Furthermore, we present a concise counterexample to illustrate the tightness of the largest range of feasible stepsize in GiPMGE. Under the assumption that the objective function satisfies the Kurdyka-{\L}ojasiewicz property, we prove that the sequence generated by GiPMGE globally converges to a critical point of the objective function. Additionally, we conduct some numerical experiments on the least squares problem with the smoothly clipped absolute deviation penalty and the nonconvex feasibility problem to demonstrate the advantage of GiPMGE.

简    介：蔡邢菊，南京师范大学教授，博士生导师。主要从事最优化理论与算法、变分不等式、数值优化方向研究工作。主持多项国家自然科学基金青年项目和面上项目多项，获江苏省科技进步奖一等奖一项，发表SCI论文50余篇。担任中国运筹学会副秘书长、算法软件与应用分会秘书长、数学规划分会常务理事，江苏省运筹学会理事长。