Novel Decomposition Techniques Enabling Scalable Computational Frameworks for Large-Scale Nonlinear Optimization Problems

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This research project aims to develop improved numerical optimization algorithms. The research considers situations in which decisions must be made in the absence of perfect information, either due to the lack of reliable data or due to unforeseen events. Most state-of-the-art methods tackle optimization in this setting by considering many potential scenarios, which can result in formulations that are too large to be solved directly. The methodology in this project is fundamentally different and aims to create new decomposition frameworks for large-scale nonlinear continuous optimization. The algorithms under development will be tested on realistic questions in electrical power systems. For example, the decomposition algorithm will be able to break down the optimization of a large-scale power grid into computations for the high-voltage transmission grid and computations related to the many distribution networks that are attached to the transmission grid. This project provides research training opportunities for a graduate student.The project aims to create novel decomposition frameworks that lead to new practical numerical algorithms able to tackle significantly larger instances of certain structured problems in nonlinear nonconvex optimization than currently possible. This will result in computational tools for the solution of stochastic optimization problems when sample average approximation gives rise to very large deterministic instances and will significantly expand the array of tractable stochastic two-stage and bi-level optimization problems. The key innovation is a smoothing technique that overcomes the predicament that optimal subsystem solutions need not be differentiable functions of the overarching system variables. In all aspects of the research, theory will be developed that characterizes the properties of problem reformulations and the convergence guarantees for new algorithms. One expected outcome of this project is high-quality open-source software for public use, capable of exploiting parallel computing resources.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.