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In this work, we propose a computationally feasible approach todetect severe multiple contingencies. We pose a contingency analysis problem using a nonlinear optimization framework, which enables usto detect the fewest possible transmission line outages resulting ina system failure of specified severity, and the most severe system failure caused by removing a specified number of transmission lines from service. Illustrations using a three bus system and the IEEE ~;30 bus system aim to exhibit the effectiveness of the proposed approach.

Many properties of nanostructures depend on the atomic configuration at the surface. One common technique used for determining this surface structure is based on the low energy electron diffraction (LEED) method, which uses a high-fidelity physics model to compare experimental results with spectra computed via a computer simulation. While this approach is highly effective, the computational cost of the simulations can be prohibitive for large systems. In this work, we propose the use of a direct search method in conjunction with an additive surrogate. This surrogate is constructed from a combination of a simplified physics model and an interpolation that is based on the differences between the simplified physics model and the full fidelity model.

Atomic scale surface structure plays an important role indescribing many properties of materials, especially in the case of nanomaterials. One of the most effective techniques for surface structure determination is low-energy electron diffraction (LEED), which can be used in conjunction with optimization to fit simulated LEED intensities to experimental data. This optimization problem has a number of characteristics that make it challenging: it has many local minima, the optimization variables can be either continuous or categorical, the objective function can be discontinuous, there are no exact analytic derivatives (and no derivatives at all for categorical variables), and function evaluations are expensive. In this study, we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods donot explicitly use derivatives, and are particularly appropriate when categorical variables are present, an important feature that has not been addressed in previous LEED studies. We have found that pattern search methods can produce excellent results, compared to previously used methods, both in terms of performance and locating optimal results.

A new direct constrained optimization algorithm for minimizing the Kohn-Sham (KS) total energy functional is presented in this paper. The key ingredients of this algorithm involve projecting the total energy functional into a sequences of subspaces of small dimensions and seeking the minimizer of total energy functional within each subspace. The minimizer of a subspace energy functional not only provides a search direction along which the KS total energy functional decreases but also gives an optimal "step-length" to move along this search direction. A numerical example is provided to demonstrate that this new direct constrained optimization algorithm can be more efficient than the self-consistent field (SCF) iteration.

This document proposes a multi-site strategy for creating a new class of computing capability for the U.S. by undertaking the research and development necessary to build supercomputers optimized for science in partnership with the American computer industry.