Joseph Czyzyk

The NEOS Server

The Network-Enabled Optimization System (NEOS) is an Internet based optimization service. The NEOS Server introduces a novel approach for solving optimization problems. Users of the NEOS Server submit a problem and their choice of optimization solver over the Internet. The NEOS Server computes all information (for example, derivatives and sparsity patterns) required by the solver, links the optimization problem with the solver, and returns a solution.

PCx: an interior-point code for linear programming

We describe the code PCx, a primal-dual interior-point code for linear programming. Information is given about problem formulation and the underlying algorithm, along with instructions for installing, invoking, and using the code. Computational results on standard test problems are reported.

PCx user guide

We describe the code PCx, a primal-dual interior-point code for linear programming. Information is given about problem formulation and the underlying algorithm, along with instructions for installing, invoking, and using the code. Computational results on standard test problems are tabulated. The current version number is 1.0.

A Study of the Augmented System and Column-Splitting Approaches for Solving Two-Stage Stochastic Linear Programs by Interior-Point Methods

Linear programs that arise in two-stage stochastic programming offer a particularly difficult test of the robustness of interior-point methods. These LPs are typically very large, yet incorporate “dense columns”—corresponding to the first-stage variables—that rule out the standard approach of solving the so-called normal equations. We compare two alternative approaches by running tests on six groups of stochastic linear programs that have been used in previous studies. We find that the augmented system approach consistently requires an amount of work that is very nearly linear in the number of scenarios, whereas the column-splitting approach requires a less predictable amount of work that grows worse than quadratically in some cases. We conclude by explaining how the differences between the two approaches can be viewed as a consequence of the way in which myopic elimination strategies deal with the block-structured matrices involved. Our analysis also leads to a useful comparison of the augmented system a...

Optimization Case Studies in the NEOS Guide

We describe several of the case studies in the NEOS Guide, a site on the World Wide Web that contains informational and educational material about optimization. These studies show how optimization relates to practical applications. They guide the user through relevant details of the application, formulation, solution, and interpretation of the results. The studies use interactivity to build intuition, allowing users to define their own problems and examine the corresponding solutions. The studies can be used for assignments in optimization and operations research courses and as small self-guided units equivalent to one or two lecture classes.