Active portfolio management has developed substantially since the formulation of the Capital Asset Pricing Model (CAPM). While the original methodology of portfolio optimization has been lauded, it is essentially an academic exercise, with practitioners eschewing the suggested weightings. There are myriad reasons for this: nonstationarity of data, insufficiency of modeling parameters, sensitivity of optimization to small perturbations, and assumption of uniform investor utility all indicate potential failures in the model.

We present historical market data to exhibit the pitfalls outlined above. From this analysis, we proceed to examine robust portfolio construction methods. One in particular is provided by Goldfarb and Iyengar. We adapt their methodology to a cross sectional model for returns and examine the performance we achieve.

The talk will describe the speaker's experience in designing and implementing optimization algorithms for applications in industry. Discussion will focus on a retail price optimization algorithm that uses stochastic methods to handle uncertainties. The project started with a textbook approach (stochastic optimization with recourse) and evolved into a special purpose solution suited to the business case. The speaker was directly involved in gathering requirements, prototyping a mathematical model and algorithmic approach, investigating issues with real world data, and writing production software for the final implementation. The completed project currently recommends optimal prices on over 10,000 items per day.

Dr. Plantenga obtained a PhD from Northwestern University in 1994 studying large-scale nonlinear optimization methods. He has developed optimization software for PeopleSoft/Oracle, Gap Inc, Ziena Optimization, and his current employer, Sandia National Laboratories.

The search for oil and gas has three objectives: to identify and evaluate hydrocarbon-bearing reservoirs; to bring hydrocarbons to the surface safely and cost-effectively, without harming the environment; and to maximize the yield from each discovery. This talk will focus on some aspects of research in applied mathematics in the area of nuclear magnetic resonance and its application to the oilfield at Schlumberger.

This seminar will focus on the life of a Mathematician in a research and development laboratory in an industrial setting. It will describe a series of applications of advanced mathematics without going into the details of the Math utilized in each application. It will give an idea of the challenges of problem solving or/and product development faced. It will also describe job functions and opportunities as a Mathematician in a Diversified Manufacturing Company.

Strictly reactive, evolutionary approaches to improving the air transport system no longer suffice in the face of the predicted growth in demand and must be supplemented with active design methods. The ability to actively design, optimize and control a system presupposes the existence of predictive modeling and reasonably well-defined functional dependencies among the controllable variables of the system and objective and constraint functions for optimization. We investigate functional relationships that govern the performance of transport systems with the aim of arriving at substantiated modeling, design optimization, and control methods.

Numerical grid generation, that is, structured grid generation, is the development of a generalized curvilinear coordinate system. Originally designed for solving computational fluid dynamics problems over oddly shaped domains, structured techniques have competed with various unstructured methods such as Voronoi or Delaunay triangulations and quadtree designs. However, the effectiveness of a given grid often depends on how it is used. For complex function visualization problems, the grid generation technique may be less important than how closely the grid lines follow the contours of the function. This talk looks at the use of a tensor product B-spline mapping to generate a boundary/contour fitted mesh that captures significant attributes such as zeros, poles, branch cuts and other singularities when the mesh is used to plot a complex function surface.

This work has been used to create over 200 interactive 3D visualizations of complex function surfaces for the NIST Digital Library of Mathematical Functions (DLMF). The NIST DLMF and its hardcopy version, the NIST Handbook of Mathematical Functions, will replace the well-known NBS Handbook of Mathematical Functions edited by Abramowitz and Stegun and first published in 1964.

Chemical spectroscopy is an invaluable tool in commerce, public safety, health care, national security, and scientific research. In most cases a measurement expert with considerable experience using an ill-defined catalog of heuristic rules is required to optimize the instrument and to interpret the data. Using an expert is expensive, not always reproducible, and introduces uncontrolled bias to the measurement process. Numerical algorithms for nonlinear optimization can supplement, and perhaps even replace, the knowledge of the expert operator. I will discuss my work with one of the most complex and fastest growing of the new chemical spectroscopies: matrix assisted laser desorption/ionization time of flight mass spectrometry (MALDI TOF MS). This technique finds broad application in both the biological and materials sciences, from drug discovery to the development of high performance plastics. I will demonstrate the application of an optimization method applied to the analysis of a synthetic polymer, one of the most difficult species to analyze by MALDI TOF MS.

Despite their obvious advantages, computer simulations also introduce many challenges. Uncertainties must be identified and quantified in order to guarantee some level of predictive of a computational model. Calibration techniques can be applied to both improve the model and to curtail the loss of information caused by using simulations in place of the actual system.

Evaluating and calibrating a computer model is dependent on three main components: experimental data, model parameters, and algorithmic techniques. Data is critical as it defines reality, and inadequate data can render model evaluation procedures useless. Model parameters should be studied to determine which affect the predictive capabilities of model and which do not. Those that do are subject to calibration. Techniques for model evaluation and calibration should both sufficiently sample the design space and limit the computational burden.

In this talk, we will discuss the problems inherent in model calibration and validation processes in terms of data, parameters and algorithms. In particular, we will focus on suitable techniques of optimization and statistics for some specific numerical models from the areas of electrical engineering, medicine, and groundwater control. We will demonstrate some successful and some not so successful approaches.