An Efficient Decomposition Algorithm for Static, Stochastic, Linear and Mixed-Integer Linear Programs with Conditional-Value-at-Risk Constraints

We present an efficient decomposition algorithm for single-stage, stochastic linear programs, where conditional value at risk (CVaR) appears as a risk measure in multiple constraints. It starts with a well-known nonlinear, convex reformulation of conditional value at risk constraints, and establishes the connection to a combinatorially large polyhedral representation of the convex feasible set induced … Read more

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 compact-sized linear optimization problems, and solves them sequentially to find the optimal solution. The problem size IEM solves in each iteration is unaffected by the size of random samples, which makes it … Read more