报告题目：A preconditioned second-order convex splitting algorithm with a difference of varying convex functions and line search

报 告 人：孙鸿鹏教授（中国人民大学）

报告时间：2025年9月9日  14:30-15:30

报告地点：格物楼528

报告摘要：

This paper introduces a preconditioned convex splitting algorithm enhanced with line search techniques for nonconvex optimization problems. The algorithm utilizes second-order backward differentiation formulas (BDF) for the implicit and linear components and the Adams-Bashforth scheme for the nonlinear and explicit parts of the gradient flow in variational functions. The proposed algorithm, resembling a generalized difference-of-convex-function approach, involves a changing set of convex functions in each iteration. It integrates the Armijo line search strategy to improve performance. The study also discusses classical preconditioners such as symmetric Gauss-Seidel, Jacobi, and Richardson within this context. The global convergence of the algorithm is established through the Kurdyka-Łojasiewicz properties, ensuring convergence within a finite number of preconditioned iterations. Numerical experiments demonstrate the superiority of the proposed second-order convex splitting with line search over conventional difference-of-convex-function algorithms. This is a joint work with Xinhua Shen and Zaijiu Shang.

报告人简介：

孙鸿鹏，中国人民大学教授，博导。2012年博士毕业于中国科学院数学与系统科学研究院，2012-2014奥地利格拉茨大学博后，研究方向反问题和图像处理。现主持国家自然科学基金面上项目、北京市自然科学基金重点项目子课题、曾主持德国洪堡基金等项目。在相关领域期刊发表论文多篇，包括权威期刊如SIAM J. Numer. Anal.，IP，SIAM SISC，SIAM MMS等。