题　目：The Role of Level-Set Geometry on the Performance of PDHG for Conic Linear Optimization

嘉　宾：Robert Freund, Professor, MIT (Mass. Inst. of Technology)

主持人：葛冬冬  教授 上海交通大学安泰经济与管理学院

时　间：2025年6月6日（周五）14:00-15:30

地　点：上海交通大学 徐汇校区安泰浩然楼308室

内容简介:

In joint work with Zikai Xiong, we consider solving huge-scale instances of (convex) conic linear optimization problems, at the scale where matrix-factorization-free methods are attractive or necessary. The restarted primal-dual hybrid gradient method (rPDHG) -- with heuristic enhancements and GPU implementation -- has been very successful in solving huge-scale linear programming (LP) problems.  Here we extend the study of rPDHG to encompass Conic Linear Optimization as well. We present a new theoretical analysis of rPDHG for general (convex) conic linear optimization and for LP as a special case thereof. We show a relationship between geometric measures of the primal-dual (sub-)level sets and the convergence rate of rPDHG. We also show how central-path-based linear transformations -- including conic rescaling -- can markedly enhance the convergence rate of rPDHG.  Last of all, we present computational results that demonstrate how rescalings can accelerate convergence to high-accuracy solutions, and lead to more efficient methods for huge-scale LP problems in particular.

演讲人简介：

Robert Freund is the Theresa Seley Professor in Management Science and a Professor of Operations Research at the MIT Sloan School of Management. 

His main research interests are in convex optimization, computational complexity and related computational science, convex geometry, large-scale nonlinear optimization, and related mathematical systems.  His more recent work is in first-order methods and their connections to statistical and machine learning. He has served as coeditor of the journal Mathematical Programming and associate editor of several optimization and operations research journals. He is the former Co-Director of MIT Operations Research Center, the MIT Program in Computation for Design and Optimization, and the former Chair of the INFORMS Optimization Section. He also served a term as Deputy Dean of the Sloan School at MIT (2008-11).

Freund received the Longuet-Higgins Prize in computer vision (2007) as well as numerous teaching and education awards at MIT in conjunction with the course and textbook (coauthored with Dimitris Bertsimas) Data, Models, and Decisions: the Fundamentals of Management Science.

Freund holds a BA in mathematics from Princeton University and an MS and a PhD in operations research from Stanford University.

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