We investigate lifting i e the process of taking a valid inequality for a polyhe dron and extending it to a valid inequality in a higher dimensional space Lifting is usually applied sequentially that is variables in a set are lifted one after the other This may be computationally unattractive since it involves the solution of an optimization problem to compute a lifting coe cient for each varia...

This paper considers the precedence constrained knapsack problem. More speci cally, we are interested in classes of valid inequalities which are facet-de ning for the precedence constrained knapsack polytope. We study the complexity of obtaining these facets using the standard sequential lifting procedure. Applying this procedure requires solving a combinatorial problem. For valid inequalities ...

Abstract. In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting setting, and earlier obtained sufficient conditions turn out not to be necessary conditions. It is also shown that these conditions simplify in certain s...