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Mathematics and Computer Science

Next-Generation Optimization under Uncertainty: Structure-Oriented Algorithms

Developing scalable algorithms and supporting convergence theory to address national infrastructure operations

The purpose of this project is to develop scalable algorithms and supporting convergence theory for extreme-scale stochastic optimization problems arising in the design and dispatch operations of national infrastructures. To this end, we will develop a new family of Newton-based, stochastic search algorithms that have a holistic view of the interactions between uncertainty modeling and stochastic optimization. The algorithms will include novel search and termination criteria that merge deterministic and probabilistic metrics. These will enable us to rapidly identify high-quality solutions and to make an adaptive trade-off between stationarity, cost confidence levels, and probabilistic constraint satisfaction.

We will also develop strategies to construct and sample misspecified and high-dimensional probability distributions such as those arising from spatiotemporal weather and network demand data. The algorithms will be implemented as part of the open-source, high-performance computing libraries TAO, PETSc, and ScalaGauss and will be tested on the Fusion and Blue Gene/P systems at Argonne National Laboratory.