This paper presents a novel range division and contraction approach for globally solving nonconvex quadratic program with quadratic constraints. By constructing new underestimating linear relaxation functions, we can transform the initial nonconvex quadratic program problem into a linear program relaxation problem. By employing a branch and bound scheme with a range contraction approach, we des...

A variableband relaxation algorithm for solving large linear systems is developed as an alternative to Gaues-Jacobi relaxation. This algorithm seeks to improve the reliability of Gauss-Jacobi relaxation by extracting a variable-sized band from the matrix and solving that band directly. This leads to a relaxation algorithm with provably better convergence p rop erties. Furthermore, this algorith...

We present and study a mixed integer programming model that arises as a substructure in many industrial applications. This model provides a relaxation of various capacitated production planning problems, more general fixed charge network flow problems, and other structured mixed integer programs. After distinguishing the general case, which is NP–hard, from a polynomially solvable case, we anal...

Linear programming (LP) relaxations are widely used to attempt to identify a most likely configuration of a discrete graphical model. In some cases, the LP relaxation attains an optimum vertex at an integral location and thus guarantees an exact solution to the original optimization problem. When this occurs, we say that the LP relaxation is tight. Here we consider binary pairwise models and de...

Gomory mixed-integer (GMI) cuts are among the most effective cutting planes for general mixed-integer programs (MIP). They are traditionally generated from an optimal basis of a linear programming (LP) relaxation of a MIP. In this paper we propose a heuristic to generate useful GMI cuts from additional bases of the initial LP relaxation. The cuts we generate have rank one, i.e., they do not use...

SNCF is a large railway transportation company that operates 365 days a year and 24 hours a day. In order to schedule a certain category of workers at train stations and ticket selling points, rosters are designed to cover a cyclical demand. However, the highly combinatorial nature of the rostering problem makes it very difficult to solve it manually, and experts spend a huge amount of time to ...

The standard technique of reduced cost fixing from linear programming is not trivially extensible to semidefinite relaxations as the corresponding Lagrange multipliers are usually not available. We propose a general technique for computing reasonable Lagrange multipliers to constraints which are not part of the problem description. Its specialization to the semidefinite {−1 1} relaxation of qua...

In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.

Production planning in flexible manufacturing system deals with the efficient organization of the production resources in order to meet a given production schedule. It is a complex problem and typically leads to several hierarchical subproblems that need to be solved sequentially or simultaneously. Loading is one of the planning subproblems that has to addressed. It involves assigning the neces...

In this paper we describe a new approach to solving the express shipment service network design problem. Conventional polyhedral methods for network design and network loading problems do not consistently solve instances of the planning problem we consider. Under a restricted version of the problem, we transform conventional formulations to a new formulation using what we term composite variabl...