We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for homogeneous cones. We identify some kn...

The linear programming problem is usually solved through the use of one of two algorithms: either simplex, or an algorithm in the family of interior point methods. In this article two representative members of the family of interior point methods are introduced and studied. We discuss the design of these interior point methods on a high level, and compare them to both the simplex algorithm and ...

As it is well-known, since the discovery of the interior-point methods linear programming (LP) is no longer synonymous with the celebrated simplex method. The interior-point methods (IPMs) have not only a better complexity bound than the simplex method (polynomial vs. exponential) but also enjoy practical efficiency and can be considerably faster than the simplex method for many (but not for al...

A large number of problems in transportation, communications and manufacturing can be modelled as network ow problems. In these problems one seeks to nd the most e cient, or optimal, way to move ow (e.g. materials, information, buses, electrical currents) on a network (e.g. postal network, computer network, transportation grid, power grid). Many of these optimization problems are special classe...

We prove a formula conjectured by Ahrens, Gordon, and McMa-hon for the number of interior points for a point connguration in R d. Our method is to show that the formula can be interpreted as a sum of Euler characteristics of certain complexes associated with the point connguration, and then compute the homology of these complexes. This method extends to other examples of convex geometries. We s...

In this work results of a comparison of ve LP codes, BPMPD, HOPDM, LOQO, LIPSOL, and SOPLEX are reported and also of the rst three as QP solvers. Since LOQO can solve general NLP problems it is in another class. For LP/QP problems it proves to be robust but it solves certain LP problems somewhat slower due to its limited presolve feature. SOPLEX as the only simplex-based program is highly compe...

An algorithm for solving linear programming problems can be used as a subroutine in methods for more complicated problems. Such methods usually involve solving a sequence of related linear programming problems, where the solution to one linear program is close to the solution to the next, that is, it provides a warm start for the next linear program. The branch and cut method for solving intege...

The use of optimization in a simulation based design environment has become a common trend in industry today. Computer simulation tools are common place in many engineering disciplines, providing the designers with tools to evaluate a design’s performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulatio...

In this paper we present the results obtained in the solution of sparse and large systems of non-linear equations by inexact Newton methods combined with an block iterative row-projection linear solver of Cimmino-type. Moreover, we propose a suitable partitioning of the Jacobian matrix A. In view of the sparsity, we obtain a mutually orthogonal row-partition of A that allows a simple solution o...