Adaptive sampling strategies for risk-averse stochastic optimization with constraints

Florian Beiser, Brendan Keith, Simon Urbainczyk, Barbara Wohlmuth

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
33 Downloads (Pure)


We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method, where the sample size used to approximate the reduced gradient is determined on-the-fly and updated adaptively. This method is applicable to a broad class of expectation-based risk measures, and leads to a significant reduction in the individual gradient evaluations used to estimate the objective function gradient. Numerical experiments with expected risk minimization and conditional value-at-risk minimization support this conclusion, and demonstrate practical performance and efficacy for both risk-neutral and risk-averse problems. Second, we propose an SQP-type method based on similar adaptive sampling principles. The benefits of this method are demonstrated in a simplified engineering design application, featuring risk-averse shape optimization of a steel shell structure subject to uncertain loading conditions and model uncertainty.
Original languageEnglish
Pages (from-to)3729-3765
Number of pages37
JournalIMA Journal of Numerical Analysis
Issue number6
Early online date19 Jan 2023
Publication statusPublished - Nov 2023


  • constrained optimization
  • portfolio optimization
  • sample size selection
  • shape optimization
  • stochastic optimization

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • General Mathematics


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