I will  present the recent work by my research group on the design, analysis, and implementation of algorithms for solvi ng 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.  I will also discuss the various extensions that my group is exploring along with other related open questions. 

Frank E. Curtis is a Professor in the Department of Industrial and Systems Engineering at Lehigh University, where he has been employed since 2009. He received his Bachelor degree from the College of William and Mary in 2003 with a double major in Mathematics and Computer Science, received his Master degree in 2004 and Ph.D. in 2007 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 from 2007 until 2009. 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. He served as the Vice Chair for Nonlinear Programming for the INFORMS Optimization Society from 2010 until 2012, and is currently very active in professional societies and groups related to mathematical optimization, including INFORMS, the Mathematics Optimization Society, and the SIAM Activity Group on Optimization.