We consider linear optimization problems over the cone of copositive matrices. Such conic optimization problems, called {\em copositive programs}, arise from the reformulation of a wide variety of difficult optimization problems. We propose a hierarchy of increasingly better outer polyhedral approximations to the copositive cone. We establish that the sequence of approximations is exact in … Read more
Let $G=(V,E)$ be a simple graph on $n$ nodes. We show how to construct a partial subgraph $D$ of the line graph of $G$ satisfying the identity: $\overline \chi(G)+\alpha(D)=n$, where $\overline \chi(G)$ denotes the minimum number of cliques in a clique partition of $G$ and $\alpha(D)$ denotes the maximum size of a stable set of … Read more
We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lov{\’a}sz’s theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a … Read more