EVENT CANCELLED 

AI4OPT Seminar Series

Thursday, Nov 16, 2023, Noon – 1:00 pm

Location: J.Erksine Love Building Room 183 (771 Ferst Dr. N.W.  Atlanta, GA 30318)

Also live streamed at: https://gatech.zoom.us/j/99381428980

Speaker: Professor Jong-Shi Pang

Heaviside Composite Optimization: Continuous meets Discrete

Abstract: This talk discusses the applications, theory, and methods for a new class of optimization problems which we call Heaviside composite optimization.  Such a constrained optimization problem has its objective and constraints defined by Heaviside composite functions.  By its name, a Heaviside composite function is the composition of a (discontinuous) Heaviside function with a multivariate function that may be nonconvex and nondifferentiable.  This research is the next chapter of the speaker's research on modern nonsmooth and nondifferentiable optimization, extended to a broad class of discontinuous functions that fuse the continuous and discrete domains. Modeling-wise, a Heaviside composite function provides a unified formulation for many important applications, such as variable and constraint selections, their extensions to switching functions, multiclass decision rules that extends binary classifications, and decision dependent conditional probabilities and conditional expectation functions. Theory-wise, a new necessary condition for a local minimizer, called epi-stationarity, can be defined by a simple lifting without hiding the constraints; this turns out to have an equivalent definition using advanced derivative concepts in variational analysis.  A novel set-theoretic property called ``convexity-like'' is key to showing epi-stationarity sufficiency.  Algorithm-wise, advances in integer programming (IP) methods and available solvers can be leveraged to improve the quality of a stationary solution, and allows (large-sized) problems, which a straightforward IP approach either fails or requires extensive effort, to be solvable within reasonable amount of time.   This very simple, yet very effective solution strategy can be applied to many other contexts such as optimization problems with complementarity constraints and optimization of conditional probability and expectation functions; these extensions are presently under study.
 
Much of this research is joint with Drs. Ying Cui (University of California at Berkeley), Junyi Liu (Tsinghua University), and Shaoning Han (University of Southern California), and involves collaboration with Dr. Yue Fang (Chinese University of Hong Kong at Shenzhen, China) on an application to a welfare economics model.
 
Bio: Elected a member of the National Academy of Engineering in February 2021 and appointed a Distinguished Professor in April 2023, Jong-Shi Pang joined the University of Southern California as the Epstein Family Chair and Professor of Industrial and Systems Engineering in August 2013. Prior to this position, he was the Caterpillar Professor and Head of the Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champagne for six years between 2007 and 2013. He held the position of the Margaret A. Darrin Distinguished Professor in Applied Mathematics in the Department of Mathematical Sciences and was a Professor of Decision Sciences and Engineering Systems at Rensselaer Polytechnic Institute from 2003 to 2007. He was a Professor in the Department of Mathematical Sciences at the Johns Hopkins University from 1987 to 2003, an Associate Professor and then Professor in the School of Management from 1982 to 1987 at the University of Texas at Dallas, and an Assistant and then an Associate Professor in the Graduate School of Industrial Administration at Carnegie-Mellon University from 1977 to 1982. During 1999 and 2001 (full time) and 2002 (part-time), he was a Program Director in the Division of Mathematical Sciences at the National Science Foundation. Professor Pang has served as the Department Academic Advisor of the Department of Mathematics at the Hong Kong Polytechnic University. 
 
Professor Pang was a recipient of the 2019 John von Neumann Theory Prize awarded by the Institute for Operations Research and Management Science (INFORMS) for his sustained contribution to multi-agent optimization and equilibrium theory and applications. Previously, he was a winner of the 2003 George B. Dantzig Prize awarded jointly by the Mathematical Programming Society and the Society for Industrial and Applied Mathematics (SIAM) for his work on finite-dimensional variational inequalities; in addition, he was a co-winner of the 1994 Frederick W. Lanchester Prize awarded by INFORMS. Dr. Pang is a Fellow of INFORMS in October 2019, and a member in the inaugural 2009 class of Fellows of SIAM. Since July 2019, he serves as the Editor-in-Chief of the prestigious SIAM Journal on Optimization. Prior to that, he was the Editor-in-Chief of the journal Mathematical Programming, Series B. He was an Area Editor of Continuous Optimization in the journal Mathematics of Operations Research from 1999 till 2006. 

Note:
Lunch will be served at the seminar. So, please stop by 15 minutes before the seminar to pick up lunch.
To continue receiving all AI4OPT seminar announcements, please sign up to the mailing list at:   https://lists.isye.gatech.edu/mailman/listinfo/ai4opt-seminars  

Videos of the past seminars can be seen on AI4OPT webpage at:   https://www.ai4opt.org/seminars/past-seminars