We present a new algorithm, Iterative Estimation Maximization (IEM), for stochastic linear and convex programs with Conditional-Value-at-Risk (CVaR) constraints. IEM iteratively constructs a sequence of compact-sized linear, or convex, 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 extreme efficient for real-world, large-scale problems. We prove that IEM converges to the true optimal solution, and give a lower bound on the number of samples required to probabilistically satisfy a CVaR constraint. Experiments show that IEM is an order of magnitude faster than the best known algorithm on large problem instances.
By: Pu Huang, Dharmashankar Subramanian
Published in: RC24535 in 2008
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .