Integer Polynomial Optimization in Fixed Dimension

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are non-negative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.Comment: In this revised version we include a stronger complexity bound on our algorithm. Our algorithm is in fact an FPTAS (fully polynomial-time approximation scheme) to maximize a non-negative integer polynomial over the lattice points of a polytop

On the complexity of nonlinear mixed-integer optimization

This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained fully polynomial time approximation schemes in fixed dimension, and to strongly polynomial-time algorithms for special cases.Comment: 26 pages, 5 figures; to appear in: Mixed-Integer Nonlinear Optimization, IMA Volumes, Springer-Verla

Geoprocessing Web Services

Since 2003, Critech has performed research on web based geoprocessing. This was before OGC started work on the Web Processing Service standards. While continuously evaluating the benefits and drawbacks of existing (open-source and commercial) GIS software packages, the operational benefits of an ESRI site license drove the development in this area. Early work focused on scripting technologies. In 2007, Critech exploited the Application Program Interfaces (APIs) of ESRI software, in particular ESRI SDE. With the (stable) release of ESRI ArcGIS Server, web geoprocessing becomes an integral part of the software. This new technology will be used by Critech in 2008. This document reports on the status of the work.JRC.G.2-Support to external securit

Computational fluid dynamics for propulsion technology: Geometric grid visualization in CFD-based propulsion technology research

The coordination is examined of necessary resources, facilities, and special personnel to provide technical integration activities in the area of computational fluid dynamics applied to propulsion technology. Involved is the coordination of CFD activities between government, industry, and universities. Current geometry modeling, grid generation, and graphical methods are established to use in the analysis of CFD design methodologies