Convexity and concavity properties of the optimal value function in parametric nonlinear programming
Journal of Optimization Theory and Applications
Sublinear upper bounds for stochastic programs with recourse
Mathematical Programming: Series A and B
Mathematics of Operations Research
Operations Research
An upper bound for SLP using first and total second moments
Annals of Operations Research
Bounding separable recourse functions with limited distribution information
Annals of Operations Research
Tight bounds for stochastic convex programs
Operations Research
Restricted-Recourse Bounds for Stochastic Linear Programming
Operations Research
Jackknife estimators for reducing bias in asset allocation
Proceedings of the 38th conference on Winter simulation
Second-Order Lower Bounds on the Expectation of a Convex Function
Mathematics of Operations Research
A Sequential Sampling Procedure for Stochastic Programming
Operations Research
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We develop an algorithm for two-stage stochastic programming with a convex second stage program and with uncertainty in the right-hand side. The algorithm draws on techniques from bounding and approximation methods as well as sampling-based approaches. In particular, we sequentially refine a partition of the support of the random vector and, through Jensen's inequality, generate deterministically valid lower bounds on the optimal objective function value. An upper bound estimator is formed through a stratified Monte Carlo sampling procedure that includes the use of a control variate variance reduction scheme. The algorithm lends itself to a stopping rule theory that ensures an asymptotically valid confidence interval for the quality of the proposed solution. Computational results illustrate our approach.