SAMPLE SIZE ESTIMATES FOR RISK-NEUTRAL SEMILINEAR PDE-CONSTRAINED OPTIMIZATION

Johannes Milz, Michael Ulbrich

Research output: Contribution to journalArticlepeer-review

Abstract

The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations 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. Numerical illustrations are presented.

Original languageEnglish
Pages (from-to)844-869
Number of pages26
JournalSIAM Journal on Optimization
Volume34
Issue number1
DOIs
StatePublished - 2024

Keywords

  • Monte Carlo sampling
  • PDE-constrained optimization under uncertainty
  • sample average approximation
  • sample complexity
  • stochastic optimization
  • uncertainty quantification

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