Title: Algorithms for Deterministically Constrained Stochastic Optimization

Abstract: I will present the recent work by my research group on the design, analysis, and implementation of algorithms for solving continuous nonlinear optimization problems that involve a stochastic objective function and deterministic constraints.  The talk will focus on our sequential quadratic optimization (commonly known as SQP) methods for cases when the constraints are defined by nonlinear systems of equations, which arise in various applications including optimal control, PDE-constrained optimization, and network optimization problems.  One might also consider our techniques for training machine learning (e.g., deep learning) models with constraints.  Much of our recent work focuses on the "fully stochastic" regime in which only stochastic gradient estimates are employed, for which we have derived convergence in expectation results and worst-case iteration complexity bounds that are on par with stochastic gradient methods for the unconstrained setting.  I will also discuss the various extensions that my group is exploring along with other related open questions.Bio: Frank E. Curtis is a Professor in the Department of Industrial and Systems Engineering at Lehigh University. He received his Bachelor degree from the College of William and Mary with a double major in Mathematics and Computer Science, received his Master degree and Ph.D. from the Department of Industrial Engineering and Management Science at Northwestern University, and spent two years as a Postdoctoral Researcher in the Courant Institute of Mathematical Sciences at New York University. 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 Advanced Scientific Computing Research program of the U.S. Department of Energy, and has received funding from various programs of the U.S. National Science Foundation, including through a TRIPODS Institute grant awarded to him and his collaborators at Lehigh, Northwestern, and Boston University. He received, along with Leon Bottou (Facebook AI Research) and Jorge Nocedal (Northwestern), the 2021 SIAM/MOS Lagrange Prize in Continuous Optimization. He was awarded, with James V. Burke (U. of Washington), Adrian Lewis (Cornell), and Michael Overton (NYU), the 2018 INFORMS Computing Society Prize. He and team members Daniel Molzahn (Georgia Tech), Andreas Waechter (Northwestern), Ermin Wei (Northwestern), and Elizabeth Wong (UC San Diego) were awarded second place in the ARPA-E Grid Optimization Competition in 2020. He currently serves as an Associate Editor for Mathematical Programming, SIAM Journal on Optimization, Mathematics of Operations Research, IMA Journal of Numerical Analysis, and Mathematical Programming Computation.