Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization

Explore a 30-minute conference talk on sample size estimates for risk-neutral semilinear PDE-constrained optimization, presented by Michael Ulbrich at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the application of the sample average approximation (SAA) approach to optimization problems governed by semilinear elliptic partial differential equations with random inputs. Learn about the construction of a compact set containing SAA critical points and the derivation of nonasymptotic sample size estimates using the covering number approach. Discover upper bounds on the number of samples required to obtain accurate critical points of risk-neutral PDE-constrained optimization problems through SAA critical points. Understand how accuracy is quantified using expectation and exponential tail bounds. Gain insights from numerical illustrations presented during the talk, which was part of the "One World Optimization Seminar in Vienna" workshop held at ESI in June 2024. The presentation also covers joint work with Johannes Milz, providing a comprehensive overview of this advanced mathematical topic.