Large-Scale Unit Commitment: Decentralized Mixed Integer Programming Approaches
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We investigate theory and application of decentralized optimization for mixed integer programming (MIP) problems. Our focus is on loosely coupled MIPs where different blocks of the problem have mixed integer linear feasible sets and a small number of linear constraints couple these blocks together. We develop decentralized optimization approaches based on Lagrangian and augmented Lagrangian duals for such MIPs. The contributions of this dissertation are a) proof of exactness of augmented Lagrangian dual (ALD) for MIPs, b) decentralized exact and heuristic algorithms for MIPs, and c) application to decentralized unit commitment (UC). We demonstrate remarkable performance of parallel implementation of the heuristic decentralized algorithm to solve large-scale UC instances. Solving ALD for MIPs in parallel , investigating ALD for (convex) mixed integer nonlinear programs, decentralized approaches for stochastic and robust MIPs and applications to other variants of UC are discussed as future research directions.