Asymptotic Results of Stochastic Decomposition for Two-Stage Stochastic Quadratic Programming

What is it about?

Convergence rates of stochastic optimization algorithms have mainly been studied for first-order methods. This paper is among few which address Stochastic Quadratic Programming, and shows that under certain reasonable assumptions, a Stochastic Decomposition algorithm yields a sublinear convergence rate for problem classes known as SQLP (quadratic first-stage and linear second stage) and SQQP (both first and second-stage models are quadratic). In addition, we suggest a stopping rule which can assess the optimality gap based on constructing consistent bootstrap estimators.

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Why is it important?

This paper is particularly important for stochastic convex programming models because the results of this paper could be easily extended to more general, constrained convex Stochastic Programming problems.