数学科学学院学术报告
Dualization: from subspace correction to operator splitting and alternating direction methods of multipliers
姜博鸥
（阿卜杜拉国王科技大学）
报告时间：2025年9月29日 星期一 下午 14：00-15：00
报告地点：腾讯会议：635-815-576 会议密码：0929
报告摘要：In this work, we demonstrate that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be derived from the framework of subspace correction methods via convex duality. To formalize this connection, we introduce the notion of dualization, a process that transforms an iterative method for the dual problem into an equivalent method for the primal problem. This concept establishes new connections across these algorithmic classes. In particular, it reveals that classical algorithms such as the von Neumann, Dykstra, Peaceman--Rachford, and Douglas--Rachford methods can be interpreted as dualizations of subspace correction methods applied to suitable dual formulations. This unified viewpoint facilitates systematic algorithm design, enables the transfer of theoretical results, and promotes new developments in convex optimization.
报告人简介：姜博鸥博士是阿卜杜拉国王科技大学科学计算与机器学习实验室许进超教授组博士后。2023年于中国科学院数学与系统科学研究院取得理学博士学位。目前主要研究方向为子空间矫正算法与算子分裂、交替方向乘子法的联系与并行化推广，并行化随机优化算法。于Journal of the Operations Research Society of China，Neural Computing and Applications等优化领域国际顶级会议发表论文，担任Domain Decomposition，Journal of Machine Learning Research等领域顶级会议和期刊审稿人。
邀请人：谢家新
