This paper introduces dual decomposition as a framework for deriving inference algorithms for NLP problems. The approach relies on standard dynamic-programming algorithms as oracle solvers for sub-problems, together with a simple method for forcing agreement between the different oracles. The approach provably solves a linear programming (LP) relaxation of the global inference problem. It leads...

We extend a well known uncrossing technique in linear programs (LPs) to work with partitions. Using this technique, we tie together three previously unrelated papers on Steiner trees, by showing that the following three values are equal: (1) the objective value of a subtour based LP by Polzin and Vahdati Daneshmand; (2) the objective value of a partition based LP by Könemann and Tan; (3) a “max...

Given a set of clients and a set of potential sites for facilities, the p-median problem consists of opening a set of p sites and assigning each client to the closest open facility to it. It can be viewed as a variation of the uncapacitated facility location problem. We propose a new formulation of this problem by a mixed integer linear problem. We show that this formulation, while it has the s...

Maximum a posteriori (MAP) inference is one of the fundamental inference tasks in graphical models. MAP inference is in general NP-hard, making approximate methods of interest for many problems. One successful class of approximate inference algorithms is based on linear programming (LP) relaxations. The augmented Lagrangian method can be used to overcome a lack of strict convexity in LP relaxat...

Split cuts constitute a class of cutting planes that has been successfully employed by the majority of Branch-and-Cut solvers for Mixed Integer Linear Programs. Given a basis of the LP relaxation and a split disjunction, the corresponding split cut can be computed with a closed form expression. In this paper, we use the Lift-and-Project framework [10] to provide the basis, and the Reduce-andSpl...

Maximum a-posteriori (MAP) inference is an important task for many applications. Although the standard formulation gives rise to a hard combinatorial optimization problem, several effective approximations have been proposed and studied in recent years. We focus on linear programming (LP) relaxations, which have achieved state-of-the-art performance in many applications. However, optimization of...

We present an in-depth theoretical, algorithmic and computational study of a linear programming (LP) relaxation to the precedence constrained single machine scheduling problem 1jprecj P j wjCj to minimize a weighted sum of job completion times. On the theoretical side, we study the structure of tight parallel inequalities in the LP relaxation and show that every permutation schedule which is co...

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the probl...

Branch-and-price is a well established technique for solving large scale integer programming problems. This method combines the standard branch-and-bound framework of solving integer programming problems with Column Generation. In each node of the branch-and-bound tree, the bound is calculated by solving the LP relaxation. The LP relaxation is solved using Column Generation. In this report, we ...