报告题目：Solving nonconvex nonsmooth minimization problems: general inertial proximal gradient type method with larger stepsize

报告专家：蔡邢菊 南京师范大学 教授

报告时间：2023年12月6日（周三）上午9：30-11:30

报告地点：南一教学楼120

报告摘要：The proximal gradient (PG) method is one of the most powerful and versatile techniques for solving nonconvex nonsmooth minimization problems and inertial strategy can significantly improve the numerical performance of PG. A general inertial proximal gradient method (GiPGM) is proved to be convergent and highly efficient for solving the sum of a smooth nonconvex function and a convex nonsmooth function. In this work, by constructing a new merit function, we prove larger parameters range can be taken without making any changes to the algorithm and assumptions, which is called general inertial proximal gradient method with larger stepsize (GiPGM-ls). Then, combining gradient extrapolation techniques, we propose a general inertial proximal type method with gradient extrapolation (GiPMGE-ls), which includes some classical algorithms as its special cases. Furthermore, we consider a more general nonconvex nonsmooth composite minimization problem，where the objective function is the sum of a smooth nonconvex function and a strictly increasing concave differentiable function composited with a convex nonsmooth function. Using the structure of this problem, we propose a general inertial composite function proximal gradient method (GiCFPGM). Under the assumption that the underlying functions satisfy the KL property and some suitable conditions on the parameters, we prove that each bounded sequence generated by the proposed methods globally converges to a critical point. In addition, we conduct some numerical experiments to demonstrate the advantage of the proposed methods.

专家简介：蔡邢菊，南京师范大学教授。主要从事最优化理论与算法、变分不等式、数值优化研究工作。主持国家青年基金一项、面上基金一项、省青年基金一项，参加国家重点项目一项，获江苏省科学技术奖一等奖一项。