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Statistical Optimality, Algorithms and Resilience in Time-Staged Stochastic Systems

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[Technical Report, Final Report]

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This project focused on mathematical decision models which capture data uncertainty. In such situations, it is almost impossible to make choices which are deterministically optimum. However, by using statistical approaches, one can make decisions which are good up to a statistically verifiable guarantee. Algorithms which provide such decisions are said to achieve some level of statistical optimality. However, because there are no absolute certainties in such a setting, it is also important that the decisions are resilient to non-optimality. In other words, the decisions should be such that the downside of facing a bad scenario is not devastating to the decision-maker. Such decisions will be referred to as resilient decisions. Our approaches were devoted to studying continuous optimization models which provide computational tools for resilient decision-making in two-stage e.g., today and tomorrow as well as multi-stage sequential decision models. Our approaches have been tested computationally, and the computational results speak to the effectiveness of these approaches. In all cases we have applied the new methods to decision problems arising in real-world settings such as network planning and system operations e.g., power.

Subject Categories:

  • Statistics and Probability
  • Numerical Mathematics

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[A, Approved For Public Release]