We introduce a natural abstraction of propositional proof systems that are based on cut- ting planes. This leads to a new class of proof systems that includes many well-known meth- ods, such as Gomory-Chvátal cuts, lift-and-project cuts, Sherali-Adams cuts, or split cuts. The rank of a proof system corresponds to the number of rounds that … Read more
We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow … Read more
Abstract This paper presents a novel formulation for the Traveling Salesman Problem (TSP), utilizing a binary list data-structure allocating cities to its leaves to form sequentially the tour of the problem. The structure allows the elimination of subtours from the formulation and at the same time reducing the number of binary variables to ${\cal O}(N\log_{2}N)$. … Read more
A big bucket time indexed mixed integer linear programming formulation for nonpreemptive single machine scheduling problems is presented in which the length of each period can be as large as the processing time of the shortest job. The model generalises the classical time indexed model to one in which at most two jobs can be … Read more
We study the generalization of split, k-branch split, and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference between a convex set and an open set with a simple geometric structure. We introduce two techniques to give precise … Read more
We consider two linear relaxations of the asymmetric traveling salesman problem (TSP), the Held-Karp relaxation of the TSP’s arc-based formulation, and a particular approximate linear programming (ALP) relaxation obtained by restricting the dual of the TSP’s shortest path formulation. We show that the two formulations produce equal lower bounds for the TSP’s optimal cost regardless … Read more
We present a quadratic outer approximation scheme for solving general convex integer programs, where suitable quadratic approximations are used to underestimate the objective function instead of classical linear approximations. As a resulting surrogate problem we consider the problem of minimizing a function given as the maximum of finitely many convex quadratic functions having the same … Read more
The classical single-band uncertainty model introduced by Bertsimas and Sim has represented a breakthrough in the development of tractable robust counterparts of Linear Programs. However, adopting a single deviation band may be too limitative in practice: in many real-world problems, observed deviations indeed present asymmetric distributions over asymmetric ranges, so that getting a higher modeling … Read more
We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a … Read more
Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank’s trading book under the Basel 2.5 Accord more than doubles that under the Basel II Accord. The significant increase in capital requirements renders it necessary for banks … Read more