Professor Freund will present his lecture titled: Level-Set Geometry and the Performance of Restarted-PDHG for Conic LP

The Lehigh ISE Department is pleased to announce that Robert M. Freund, Theresa Seley Professor in Management Science and a Professor of Operations Research at the MIT Sloan School of Management, will give the Spencer C. Schantz Technical Talk titled Level-Set Geometry and the Performance of Restarted-PDHG for Conic LP on Thursday, April 11, 2024, from 11:00 a.m. – 12:00 p.m. in Mohler Laboratory room 453, 200 West Packer Avenue, Bethlehem, PA.

A luncheon welcoming Prof. Freund and celebrating the graduation of the Lehigh ISE UG and Master’s students (May and August of 2024) will be served for faculty and students on the same day, Thursday, April 11, 2024, at Zoellner Arts Center, Butz Lobby (2nd Floor), 420 E. Packer Avenue, Bethlehem, PA 18015 from 12:15 p.m. to 1:45 p.m.

This is a time for students to mingle with classmates and faculty, and proudly acknowledge the culmination of their academic journey before they embark on the next exciting chapter of life. 

Registration is required for both events no later than April 1, 2024.

  • To register for the Technical Talk, click here.
  • To register for the ISE Graduation Party & Luncheon, click here

If you do not have a Google account, please email to register.

If you cannot attend in person, please request the Zoom link and it will be emailed to you.



We discuss our recent research aimed at solving truly huge-scale convex optimization problems, at the scale where matrix-factorization-free methods are attractive/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; however, its application to more general convex conic optimization problems is not so well-studied. We analyze the theoretical and practical performance of rPDHG for general (convex) conic optimization – with LP as a special case. We show a relationship between the geometry of the primal-dual (sub-) level sets W_e and the convergence rate of rPDHG. Specifically, we prove a bound on the convergence rate of rPDHG that improves when there is a primal-dual sublevel set W_e for which (i) W_e is close (in Hausdorff distance) to the optimal solution set, and (ii) the ratio of its diameter to its “conic radius” is small.  In the special case of LP problems, the performance of rPDHG is bounded only by this ratio applied to the sublevel set corresponding to the second-best extreme point. We note that in practice this ratio can take on extreme values and, in such cases, result in poor performance of the rPDHG both in theory and in practice. To address this issue, we show how central-path-based linear transformations – including conic rescaling – can markedly enhance the convergence rate of rPDHG.  We also present computational results that demonstrate how such rescalings can accelerate convergence to high-accuracy solutions, and lead to more efficient methods for huge-scale linear and conic optimization problems. This is joint work with Zikai Xiong.



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 co-editor 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. 


Lehigh ISE Spencer C. Schantz Distinguished Lecture Series:

This lecture series is endowed in the name of the late Spencer C. Schantz, who graduated from Lehigh in 1955 with a B.S. in Industrial Engineering. Following progressive responsibilities with several electrical manufacturing companies, in 1969 he founded U.S. Controls Corporation and became its first CEO and President. The Spencer C. Schantz Distinguished Lecture Series was established by his wife Jerelyn as a valuable educational experience for faculty, students, and friends of Lehigh’s Industrial and Systems Engineering department.