We introduce adaptive sampling methods for risk-neutral and risk-averse
stochastic programs with deterministic constraints. In particular, we propose a
variant of the stochastic projected gradient method where the sample size used
to approximate the reduced gradient is determined a posteriori and updated
adaptively. We also propose an SQP-type method based on similar adaptive
sampling principles. Both methods lead to a significant reduction in cost.
Numerical experiments from finance and engineering illustrate the performance
and efficacy of the presented algorithms. The methods here are applicable to a
broad class of expectation-based risk measures, however, we focus mainly on
expected risk and conditional value-at-risk minimization problems
