Daniel Bienstock We extend work on generating relaxations of simple sets with guaranteed bounds. Citation Unpublished. Columbia University, July 2008. Article Download View Tightening simple mixed-integer sets with guaranteed bounds
We present experimental results on portfolio optimization problems with return errors under the robust optimization framework. We use several a histogram-like model for return deviations, and a model that allows correlation among errors, together with a cutting-plane algorithm which proves effective for large, real-life data sets. Citation Columbia Center for Financial Engineering Report 2007-01 Columbia … Read more
A classical theorem in Combinatorial Optimization proves the existence of fully polynomial- time approximation schemes for the knapsack problem. In a recent paper, Van Vyve and Wolsey ask whether for each 0 < epsilon ≤ 1 there exists an extended formulation for the knapsack problem, of size polynomial in the number of variables and/or 1/epsilon ... Read more
This paper considers how to optimally set the basestock level for a single buffer when demand is uncertain, in a robust framework. We present a family of algorithms based on decomposition that scale well to problems with hundreds of time periods, and theoretical results on more general models. Citation CORC report TR-2005-09, Columbia University, November … Read more
We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks subject to multiple scenarios of externally caused damage. We present computation with networks with up to 600 nodes and 827 edges, and many thousands of damage scenarios. Citation CORC Report TR-2005-07, Columbia University Article Download View Using mixed-integer programming … Read more
We adapt a method due to Nesterov so as to obtain an algorithm for solving block-angular fractional packing or covering problems to relative tolerance epsilon, while using a number of iterations that grows polynomially in the size of the problem and whose dependency on epsilon is proportional to 1/epsilon. Citation CORC report TR-2004-09, Computational Optimization … Read more
We show that for any fixed rank, the closure of a set covering problem (and related problems) can be approximated in polynomial time — we can epsilon-approximate any linear program over the closure in polynomial time. Citation CORC report TR-2003-01, Computational Optimization Research Center, Columbia University Article Download View Approximate fixed-rank closures of set covering … Read more