We use a decomposition approach to solve two types of realistic problems: block-angular linear programs arising in energy planning, and multicommodity network problems arising in capacity planning for survvable telecommunication netwroks. Decomposition is an algorithmic device that breaks down...

This paper presents a new primal-dual algorithm for solving a class of monotropic programming problems. This class involves many problems arising in a number of important applications in telecommunications networks, transportation and water distribution. The proposed algorithm is inspired by...

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 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...

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

We analyze the process of a two cut generation scheme in the analytic center cutting plane method. We propose an optimal restoration when the two cuts are central.

In this paper we consider a new analytic center cutting plane method in a projective space. We prove the efficiency for the general scheme and show that these results can be used in the analysis of a feasability problem, the variational inequality problem and the problem if constrained...

In this paper, we discuss the optimal design of telecommunications networks prone to failure. The problem concerns mid-range planning objectives. The purpose of the model is to give insight on the cost of protecting the network against failures by balancing the choice of a base routing of the...

In this paper we study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratric form. We show that the central path of these augmented barrier functions can be traced with linear speed. We also study the...

We describe the analytic center cutting plane method and its relationship to classical methods of nondifferentiable optimization and column generation. Implementations issues are also discussed, and current applications listed.