Announcement Detail
Thursday, November 13, 2025
3pm EST
Join via Zoom: https://us06web.zoom.us/j/
USACM UQ Virtual Seminar
An inexact trust-region algorithm for nonsmooth risk-averse PDE-constrained optimization
Speaker
Drew P. Kouri, Sandia National Laboratories
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.
Upcoming webinar speakers:
Thursday, December 11: Ionut-Gabriel Farcas, Virginia Tech
Thursday, January 8: Thomas Swinburn, University of Michigan
Monday, February 8: Wei Chen, Northwestern University
Thursday, March 12: Hannah Lu, The University of Texas at Austin
Thursday, April 16: Jinlong Wu, University of Wisconsin-Madison