Applied & Computational Mathematics seminar: Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization

Speaker: Johannes Milz, Georgia Tech 

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

Abstract:  We apply the sample average approximation (SAA) approach to risk-neutral optimization problems governed by semilinear elliptic partial differential equations (PDEs) with random inputs. After constructing a compact set that contains the SAA critical points, we derive nonasymptotic sample size estimates for SAA critical points using the covering number approach. Thereby, we derive upper bounds on the number of samples needed to obtain accurate critical points of the risk-neutral PDE-constrained optimization problem through SAA critical points. We quantify accuracy using expectation and exponential tail bounds.  We present numerical illustrations. 

This is joint work with Michael Ulbrich.

Time:  Friday, September 15, 2023, 10:00am-11:00am

Place:  Zoom