I will motivate and provide an overview of recent efforts in my research group on the design and analysis of noisy and stochastic-gradient-based algorithms for solving constrained optimization problems. I will also share a more detailed look at a recent project on the challenge of active-set identification by noisy and stochastic algorithms. Identifying the constraints that are active at a solution of an optimization problem is important both theoretically and practically, such as for certifying optimality and sensitivity analysis. I will show how state-of-the-art identification techniques can be extended from deterministic to noisy and stochastic settings, and demonstrate our results with a constrained supervised learning problem.
Frank E. Curtis is a Professor in the Department of Industrial and Systems Engineering at Lehigh University. He received his PhD degree from the Department of Industrial Engineering and Management Science at Northwestern University and was a Postdoctoral Researcher in the Courant Institute of Mathematical Sciences at New York University prior to his position at Lehigh. His research focuses on the design, analysis and implementation of numerical methods for solving large-scale nonlinear optimization problems. He received an Early Career Award from the DOE Advanced Scientific Computing Research (ASCR) program, and has received funding from various programs of the U.S. National Science Foundation (NSF), including through a TRIPODS Phase I grant. He has also received funding from the U.S. Office of Naval Research (ONR), the Air Force Office of Scientific Research (AFOSR), and DoE’s Advanced Research Projects Agency-Energy (ARPA-E). He received, along with L. Bottou (Meta AI) and J. Nocedal (Northwestern), the 2021 SIAM/MOS Lagrange Prize in Continuous Optimization. He received, with J. Burke (U. Washington), A. Lewis (Cornell), and M. Overton (NYU), the 2018 INFORMS Computing Society Prize. He currently serves as Area Editor for Mathematics of Operations Research and Mathematical Programming Computation, and serves as an Associate Editor for Mathematical Programming, SIAM Journal on Optimization, Operations Research, and IMA Journal of Numerical Analysis.