CSE Distinguished Seminar | Drew Kouri

Abstract

Many practical problems require the optimization of systems of PDEs with uncertain inputs such as noisy problem data, unknown operating conditions, and unverifiable modeling assumptions. In this talk, we formulate these problems as infinite-dimensional, risk-averse stochastic programs for which we minimize a quantification of risk associated with the system performance. For many popular risk measures, the resulting risk-averse objective function is not differentiable, significantly complicating the numerical solution of the optimization problem. Unfortunately, traditional methods for nonsmooth optimization converge slowly (e.g., sublinearly) and consequently are often intractable for problems in which the objective function and any derivative information is expensive to evaluate. To address this challenge, we introduce a novel trust-region algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the primal-dual risk minimization algorithm and employs smooth approximate risk measures at each iteration. In addition, this algorithm permits and rigorously controls inexact objective function value and derivative (when available) computations, enabling the use of inexpensive approximations such as adaptive discretizations. We discuss convergence of the algorithm under mild assumptions and demonstrate its efficiency on various examples from PDE-constrained optimization.

Bio

Drew Kouri is a staff member in the Optimization and Uncertainty Quantification department at Sandia National Laboratories and his research focuses on the analysis and efficient numerical solution of large-scale PDE-constrained, nonsmooth, and stochastic optimization problems.  Dr. Kouri was awarded the DOE Early Career Award in 2021. Dr. Kouri received his BS and MS in mathematics from Case Western Reserve University, and his MA and PhD in Computational and Applied Mathematics from Rice University.  Before joining Sandia, Dr. Kouri was the J. H. Wilkinson Fellow at Argonne National Laboratory.