Jong-Shi Pang is the Epstein Family Chair and Distinguished Professor of Industrial and Systems Engineering at the University of Southern California. He is a world leader in optimization and computational methods. His research focuses on the mathematical modeling and analysis of a wide range of complex engineering and economic systems, with a focus on operations research, single-agent optimization, equilibrium programming, noncooperative game theory, and constrained dynamical systems. Prof. Pang is a member of the National Academy of Engineering and a Fellow of the Institute for Operations Research and Management Science (INFORMS). Numerous awards have recognized his research.

This talk introduces the topic of Heaviside composite optimization and briefly covers its many facets: breadth in modeling, roles in old and new applications, theory of optimizers and stationary solutions, bridge with discrete optimization, and the progressive integer programming method. By definition, a univariate Heaviside function is the (discontinuous) indicator of an interval. By its name, a Heaviside composite function is the composition of a Heaviside function with a continuous multivariate function that may be nonconvex and nondifferentiable. While very natural in modeling many physical phenomena, a Heaviside composite optimization problem, possibly with Heaviside composite functional constraints, has never been formally studied. Our work aims to fill this void with a comprehensive research program covering the applications, theory, and algorithms for this novel class of very challenging optimization problems.

This research has benefitted from previous collaboration with Ying Cui (UC Berkeley), Yue Fan (CUHK-SZ), Shaoning Han (NUS), Junyi Liu (Tsinghua), and Xinyao Zhang (USC), and is presently being organized in a monograph co-authored with Junyi Lui.