Frank Curtis

Frank E. Curtis is a Professor in the Department of Industrial and Systems Engineering at Lehigh University. His research focuses on the design, analysis, and implementation of numerical methods for solving large-scale continuous optimization problems. His work has been funded by the National Science Foundation (NSF), Department of Energy (DOE), and Department of Defense (DOD), including an Early Career Award from the Advanced Scientific Computing Research (ASCR) program of the DOE and a TRIPODS Phase I grant from the NSF. He received, along with Leon Bottou (Meta AI) 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 currently serves as Area Editor for Continuous Optimization for Mathematics of Operations Research and serves as an Associate Editor for Mathematical Programming, SIAM Journal on Optimization, Operations Research, IMA Journal of Numerical Analysis, and Mathematical Programming Computation.

Title of talk: Limited-Memory BFGS with Displacement Aggregation

I will discuss a recent extension of the limited-memory B-Goldfarb-GS (BFGS) method for approximating (inverse) Hessian matrices within a descent method for solving continuous, potentially nonconvex optimization problems. The main feature of the approach is a strategy for aggregating exact curvature information into a smaller number of pairs. This allows, for example, one to achieve superlinear convergence within an L-BFGS scheme as long as a sufficiently large (but finite) number of pairs are maintained. The results of numerical experiments show that aggregation within an adaptive L-BFGS method can lead to better performance than standard L-BFGS.