Adaptive sampling strategies for risk-averse stochastic optimization with constraints

Abstract

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.

References in corpus (2)

• Risk-averse design of tall buildings for uncertain wind conditions
• Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming

Cited by in corpus (4)

• Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization
• Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method
• Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces
• Stochastic ISTA/FISTA Adaptive Step Search Algorithms for Convex Composite Optimization