Iterative estimation maximization for stochastic linear programs with conditional value-at-risk constraints

We present a new algorithm, iterative estimation maximization (IEM), for stochastic linear programs with conditional value-at-risk constraints. IEM iteratively constructs a sequence of linear optimization problems, and solves them sequentially to find the optimal solution. The size of the problem that IEM solves in each iteration is unaffected by the size of random sample points, which makes it extremely efficient for real-world, large-scale problems. We prove the convergence of IEM, and give a lower bound on the number of sample points required to probabilistically bound the solution error. We also present computational performance on large problem instances and a financial portfolio optimization example using an S&P 500 data set.