This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and...

A new concept is proposed for linking algebraic modeling languages and the structure exploiting solver.

Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report hereon a deterministic equivalent linear programming model of 1,111,112 constraints and...

This paper deals with the sizing of telecommunications networks offering private line service to a few clients. The clients ask for some transfer capacity between some pair of nodes, but their demand is uncertain. In case of high demand and insufficient capacity, some clients may be denied the...

In this paper we give an overview of the mostimportant characteristics of advanced implementations of interior point methods.

This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classicla decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a...