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...

Two new subroutines, SPLITDAT and DECOMP, have been created in the GAMS I/O library. The aim of these subroutines is to provide the GAMS user with the possibility of using Benders and other decomposition algorithms within the Gams modeling language framework.

The capacitated multi-item lot sizing problem consists of finding a production schedule that minimizes over a finite number of periods the total production, holding inventory, and setup costs subject to demand and capacity constraints. Approximate solutions can be obtained by heuristics. In this...

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 homogeneous analytic center cutting plabne method in a projective space. We describe a general scheme that uses a homogeneous oracle and computes an approximate analytic center at each iteration. This technique is applied to a convex feasibility problem, to...

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

In the framework of regression, consider the set of regression submodels. By submodel, we mean on e or more response variables and a subset of the potential regressors. Imagine the submodels as a ponts in some space. How can we "project" these ponts onto a map so as to visualize and compare...

This article gives results specifically related to the last principal component. This linear combination of variables plays an important role when one tries to fit a hyperplane to a cloud of points. In data analysis, variables are often subject to a linear transformation. The results that we...

WE analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The dircetion is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal...

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...