报告题目：An Augmented Lagrangian Primal-Dual Semismooth Newton Method for Multi-Block Composite Optimization

报告人：户将 助理教授 （清华大学 数学科学中心）

报告时间：2025年12月29日（星期一）10:30-11:30

报告地点：数学科学学院114（小报告厅）

校内联系人：肖现涛 教授     联系方式：84708351-8312

报告摘要：In this talk, we present a novel primal-dual semismooth Newton method for solving linearly constrained multi-block convex composite optimization problems which include commonly used models in image processing and conic programming. First, a differentiable augmented Lagrangian (AL) function is constructed by utilizing the Moreau envelopes of the nonsmooth functions. It enables us to derive an equivalent saddle point problem and establish the strong AL duality under the Slater’s condition. Consequently, a semismooth system of nonlinear equations is formulated to characterize the optimality of the original problem instead of the inclusion-form KKT conditions. We then develop a semismooth Newton method, called ALPDSN, which uses second-order steps and a nonmonotone line search based globalization strategy. Through a connection to the inexact first-order steps when the regularization parameter is sufficiently large, the global convergence of ALPDSN is established. Under the regularity conditions, partial smoothness, the local error bound, and the strict complementarity, we show that both the primal and the dual iteration sequences possess a superlinear convergence rate. Numerical results on semidefinite programming on Mittelmann benchmark are presented to demonstrate the high efficiency and robustness of our ALPDSN.

个人简介：户将，清华大学数学科学中心助理教授。他的主要研究兴趣包括流形优化和机器学习。目前在SIAM 系列、NM、MOR、IEEE 系列、JMLR 和NeurIPS 等期刊和会议发表20 余篇论文，获得国际信号处理会议ICASSP 2024 唯一最佳论文奖。参与编写教材《最优化：建模、算法与理论》和《最优化计算方法》。