We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of...

In this paper we consider the problem of k-partitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition, and the objective of minimizing the sum of the costs of the edges between the subsets of the partition. Based on a study of...

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing,...

In this survey we address three of the principle algebraic approaches to integer programming. After introducing lattices and basis reduction, we first survey their use in integer programming, presenting among others Lenstra's algorithm that is polynomial in fixed dimension, and the solution of...

A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, y T A integral such that y T b is fractional. We extend this result to systems that both have...

Dieser in Teilen essayistisch gehaltene Aufsatz greift die aktuell geführte Diskussion über die Veränderung der betrieblichen Organisation von Erwerbsarbeit in Zeiten eines "flexiblen Kapitalismus" (Sennett 1998) auf und wirft einen Blick auf zentrale Merkmale, Ursachen und Konsequenzen...

A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, yTA integral such that yT b is fractional. We extend this result to systems that both have...

Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more...