The paper is a simplified exposition of an early combined phase I-phase II method for linear programming. The method works from an infeasible start. Besides, there is no need for regularity conditions if the method is applied to a primal-dual formulation.

We propose an alternative apporach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. The associated objectiev value is doubly random, since it depends two...

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...

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...

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...

The aim of this paper is to propose a method for coupling national energy models, to identify the dividends of international cooperation in atmospheric pollution abatement and efficient energy use. It indicates also how to solve the resulting large-scale multinational model. It stimulates...