Dantzig--Wolfe Decomposition is recognized as a powerful, algorithmic tool for solving linear programs of block-angular form. While use of the approach has been reported in a wide variety of domains, there has not been a general implementation of ...

Efficient methods for solving linear-programming problems in exact precision rely on the solution of sparse systems of linear equations over the rational numbers. We consider a test set of instances arising from exact-precision linear programming and ...

This article considers the application of a primal nested-decomposition method to solve staircase linear programs (SLPs) on distributed-memory, multiple-instruction-multiple-data computers. Due to the coupling that exists among the stages of an SLP, a ...

Two modifications of Bartels and Conn's algorithm for solving linearly constrained discrete l₁ problems are described. The modifications are designed to improve performance of the algorithm under conditions of degeneracy.

The main computational work in interior-point methods for linear programming (LP) is to solve a least-squares problem. The normal equations are often used, but if the LP constraint matrix contains a nearly dense column the normal-equations matrix will be ...

This article develops an affine-scaling method for linear programming in standard primal form. Its descent search directions are formulated in terms of the null-space of the linear programming matrix, which, in turn, is defined by a suitable basis ...

If A is the (sparse) coefficient matrix of linear-equality constraints, for what nonsingular T is A = TA as sparse as possible, and how can it be efficiently computed? An efficient algorithm for this Sparsity Problem (SP) would be a valuable preprocessor ...

This describes enhancements to provide more advanced computer-assisted analysis of instances of linear programming models. Three categories of enhancements are described: views, engines for obtaining information, and rule-based advising. Examples of ...

Research in network optimization has reached the stage where large-scale problems-linear or non-linear, pure or generalized-are solved very efficiently with minimal computing resources. Representing such problems for solution on the computer, however, ...

In processing networks, ordinary network constraints are supplemented by proportional flow restrictions on arcs entering or leaving some nodes. This paper describes a new primal partitioning algorithm for solving pure processing networks using a working ...

We describe a collection of modules designed to facilitate the implementation of optimization (LP) algorithms that must solve one or more linear programs in a suitably coordinated sequence. Our collection also provides a basis for discussing some of the ...

Many planning methods are based on mathematical modeling. A multitude of computer aids covers different facets of the planning activity: data management, linear programming, statistical analysis, graphics, and word processing. However, the diversity and ...

This paper examines mathematical programming software in the context of model management and decision support. The concept of a model management system (MMS) is introduced and compared to traditional modeling systems. An MMS is seen as a much more ...

An algorithm is presented for finding a root of a real function. The algorithm combines bisection with second and third order methods using derivatives estimated from objective function values. Globaql convergence is ensured and the number of function ...

In this paper we discuss the implementation of a primal simplex algorithm for network problems in the MPSIII mathematical programming system. Because of the need to interface with the rest of the MPS this implementation is unorthodox, but computationally ...