We present a polyhedral study of the complementarity knapsack problem, in which no auxiliary binary variables are introduced, but rather the inequalities are derived in the space of the continuous variables. Citation School of Industrial and Systems Engineering, GA Tech, under review Article Download View Facets of the Complementarity Knapsack Polytope
We define the concept of a computational grid, and describe recent work in solving large and complex optimization problems on this type of platform; in particular, integer programming, the quadratic assignment problem, and stochastic programming problems. This article focuses on work conducted in the metaneos project. Citation Preprint, Mathematics and Computer Science Division, Argonne National … Read more
The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n >= 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using … Read more
We study how the lift-and-project method introduced by Lov\’az and Schrijver \cite{LS91} applies to the cut polytope. We show that the cut polytope of a graph can be found in $k$ iterations if there exist $k$ edges whose contraction produces a graph with no $K_5$-minor. Therefore, for a graph with $n\ge 4$ nodes, $n-4$ iterations … Read more