金年会jinnianhuicom学术报告
An Augmented Lagrangian Primal-Dual Semismooth Newton Method for Multi-Block Composite Optimization
户将
（清华大学）
报告时间：2025年11月20日 星期四 下午 15：30-16：30
报告地点：沙河校区E806
报告摘要：In this talk, we develop 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 purely 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 and provide concrete examples where these regularity conditions are met. Numerical results on semidefinite programming on Mittelmann benchmark are presented to demonstrate the high efficiency and robustness of our ALPDSN.
报告人简介：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最优化方法与理论和机器学习。目前在SIAM 系列、Numer. Math.、Math OR、IEEE 系列、JMLR 和NeurIPS 等期刊和会议发表论文，参与编写教材《最优化：建模、算法与理论》和《最优化计算方法》。
邀请人：谢家新
